Hmm. After having just finished the author's more recent manga, Shimeji Simulation, I have to say I think I agree with Mast_Chacha's interpretation of the ending. In Shimeji Simulation, we find out that the world is a virtual simulation stored in a supercomputer floating in space that holds the souls of all humanity after a plague and then a great war. Additionally, in the manga we see Chito and Yuuri in the world. While this could just be a throw-in for fans of Girls' Last Tour, the stories of both of the worlds seem to line up well. The plague and then great war happened, throwing humanity into a death spiral which they escaped by virtualizing their souls and heading off into space, which is why in GLT we don't see any corpses around the world. This would also be supported by the fact that in the GLT chapter with the rocket we see that the third rocket launched by humanity is still out there in space, somewhere far off. Then, at the end of GLT as Chito and Yuuri finally reach the highest point in the city, they come across the mysterious black stone that's mentioned, shown to contain machine code, but never elaborated upon. I would say that's most likely a transmitter, considering it's the only structure so high up. Chito and Yuuri, after waking up from their sleep, decide to investigate what the thing is (as we can see by the fact that in the final frame of the Volume 6 extra chapter there's a good deal of the face of the structure that has been wiped clean of snow), activate it, and have their souls virtualized and sent to the spacecraft, which is why they show up in Shimeji Simulation. I could very well be wrong about this and just hoping that the two girls survive, but at the same time it seems plausible to me that this could be the intended chronology.
Out of your three pieces of supporting evidence: the second is wrong since we know humanity kept moving back down the tower so it makes sense why Chito and Yuri did not come across corpses.
Furthermore, Chito and Yuuri emerges from a lower floor that is similar to WW2, just before the birth of the Atomic Age, Space Age, and Computer Age. Their journey parallels non-existence at birth arriving to the non-existence at death, it represents the mortality of humanity. However, humanity's mortality also lies with it a piece of hope. Humanity's downfall does not end with its corruption by all the power it has accumulated and unresolved hatreds then degenerates back down to its origin, but with an innocent new generation that rediscovers all of humanity's accomplishments celebrating how far we've come. This is, in my opinion, why Shimeji Simulation takes place in a world beyond war and death because both war and death has already been finished in Girl's Last Tour.
Moreover, your theory makes no sense because there is nothing to suggest the black rock is a transmitter or a machine of any sort. It is an otherworldly "structure" that is reminiscent of other structures seen in Shimeji Simulation because that's what its supposed to be. By climbing up to the final floor, Chito and Yuuri have left behind the world of war and death and into the world that is elaborated upon in Shimeji Simulation. But, this doesn't mean Chito and Yuuri in Girl's Last Tour are the same couple as the neighbors in Shimeji Simulation, because the two mangas are separate worlds where Tkimz can explore the philosophical ideas unique to each one.
I'm not sure what you mean by "humanity kept moving back down the tower", could you elaborate? As for Chito and Yuuri starting off in a lower floor with WWII-esque technology, from their flashbacks we see that they come from a survivor community. With the vast majority of humanity dead, it makes sense that the survivors would only make use of technology that's easy to understand and utilize as opposed to more complex computer-based stuff. As for the black rock being a transmitter/computer, we see in the bonus chapter that a robot writes "machine words" out on a table, which are identical in structure to those expressed on the black rock in the volume 6 tankobon extra chapter. I see no reason why the black rock would have machine code on it if it wasn't itself a machine. The fact that we see these symbols in ShimSim when the world's being changed only further suggests this fact considering that the world of ShimSim is in a computer simulation and thus the world's rules would be written in code. As for it being a transmitter specifically, my main evidence for that is that it's the only thing at the very top of the world, the closest to space (where it would be the easiest to send signals to a floating supercomputer). What else would a lone piece of machinery on the roof be used for?
As for whether or not the Chito and Yuuri of ShimSim and GLT are the same people, yeah, who knows. Could just be a cameo from the author because the two characters are popular. But considering how much the backstory of ShimSim parallels with the story of GLT and for the reasons I've previously listed, in my mind it seems likely.
Literally that, humanity continued the war by traveling down the tower to keep fighting with older technology once the newer technology was destroyed. Despite all the destruction and regression, humanity still chose to continue war.
Your second point is yet another massive jump in logic that lands into a bottomless pit. So both the rock and table has been inscribed with "machine words", but that doesn't lead any credence to the possibility of the rock being a transmitter capable of uploading electronic beings to a specific satellite far away in outer space more so than the table is. All the "machine words" proves is that the rock, like the table, is a solid surface to write things on, and that's it.
Lastly, the reason that rock is there is for the same reason those stairs are there: humanity ended with unfinished aspirations and not because it had accomplished some ultimate goal it had set out for itself. In fact, Chito and Yuuri's last words reflect this same exact meaning, rather than thinking of how to spend their final moment upon finishing their journey, they anticipated waking-up tomorrow, always believing in life. This is what Tkimz wants the reader to learn from Chito and Yuuri's "Last Tour": humans should not live life expecting how it will end.
I can agree with your point about humanity going down the tower and fighting with older tech, it would make sense if you were in a war that destroyed a huge chunk of your population to switch to more reliable and easily-producible weapons instead of ones that require knowledge from people who are probably all dead. Not sure how that proves my point about the plague and then a great war mentioned in ShimSim lining up with the GLT world well wrong.
Dude, you really need to stop acting like I'm directly insulting you or the creator. "A massive jump in logic that lands into a bottomless pit." Calm down man. How on earth is it a jump in logic to assume that an object with machine code written on it would be a machine, rather than a large, inanimate rock that somehow got up to the highest point of the world (it wouldn't even fit up the staircase) and then had this code written on it for no reason, the writing being uncovered in the very end frame for also no reason. As for it being a transmitter specifically, I've already explained my logic on that, and while of course it's a theory and not a fact, I really don't see why you see it as so unlikely.
As for the fact that you're explaining all this away by saying that it's just symbolism involved in the author's takeaway message for the book, is there anywhere that they've confirmed any of what you're saying, or is this just your takeaway from the series that you're expecting others to take as fact? Personally I had different takeaways from it, though yours certainly isn't wrong, people can get different messages from media. And even with your idea of the author's message, how on earth is putting a big black rock and then putting machine code on that rock important for that? I totally get how there being nothing on the roof represents humanity ending with unfinished aspirations, but that doesn't explain at all why there's a rock with machine code on it.
Nothing in what I said indicates that I'm acting insulted. All I said is that your theory is nuts. After you yourself brought up another instance of an object etched with machine language was a table, it only makes sense to believe that rock is just as inanimate. That rock is there for the same reason those stairs climb to nowhere, they were never completed, never to fulfill an intended purpose we will never know about. So your reason why that rock is a transmitter, the machine code and its position, can be debunked.
Also, you accusing me of "explaining all this away by saying that it's just symbolism" is entirely disingenuous. Never have I claimed the rock is "just symbolism". Saying the rock being part of an unfinished building next to an unfinished flight of stairs all atop an unfinished floor juxtaposed by Chito and Yuuri falling asleep right next to it similarly with aspirations for tomorrow never to be fulfilled is what I believe to be an intentional choice by the author and further supports my explanation for what the rock is. If you disagree, fine. Leave counter-evidence as to why it's all a meaningless coincidence. But don't just wave points away as "just symbolism" without critiquing them. I agree people can come away from media interpreting different messages, all I'm doing is proposing an alternative interpretation based on evidence that debunks yours.
As for why there's machine code: Maybe a robot wrote it there when he and his human friends were constructing the final floor? Maybe they wrote it long after the humans were gone? Possibly, as a message for future robots who might happen across it? Might be graffiti? Or maybe for the same reasons why Chito and Yuuri left their drawing in that art gallery despite knowing no human would ever see it? It's very open-ended, but it can't be a transmitter not because I am the only correct explanation but because there is textual evidence that points away from the rock being a transmitter.
]They lived happily, it's very sad but it was an inevitable ending, I imagined it would end that way, and honestly, it was the most peaceful way possible... I love both of them very much