Hades if we go to such a broad category where SAO is an isekai then Inuyasha and Ryuuroden would also be considered an isekai.
Of those three overlord did come out before Mushoku however I believe slime came out only a few months after it. A lot of the other series I mentioned did come out before it though like Problem children and Familiar of Zero.
Yes, those are isekai. And if you want to try to define a subgenre of isekai, go for it. Get people to listen to you. I know what I think of it, though. And I don't think the way the character is summoned is genre-defining. It's a method for reaching the start of the plot, but doesn't define how it plays out or what kind of story it is. Well, usually.
Familiar of Zero is one of the most influential works in the Japanese isekai scene, but I find it often forgotten in discussions about the genre, even when it's talking about older works. It created so much fanfiction that many of the authors of those fanfics went on to write their own original (more or less) isekai stories. Mushoku, for instance.
Problem Children has a relatively unique world, but I never hear anyone talk about it. Which is a shame, really.
And as I said, Slime and Overlord fit other subgenres of isekai. Those are more focused on the monster and villain side of things, while Mushoku is more focused on overpowered heroes. But at the end of it, arguing that something is more popular doesn't mean something else isn't popular or influential. Personally I'm just going by what I've read others regard as being influential, since for the most part we're talking about Japanese works here, and most of us don't know all that much about how the Japanese view their works.
Edit: also Tsuki ga Michibiku Isekai Douchuu also came out before Mushoku and that series is amazing. I 100% recommended reading that novel as it’s so dam fun to read
I've read part of it, but I've also heard it gets darker and darker, which may or may not be true, but if it is, I don't think it's for me.
I don’t think anyone wants to list SW and ST as isekai do you?
Why? Is there a problem including lots of works to a genre? I mean, I don't think they fit for other reasons, but I don't see why there has to be such gatekeeping.
The same applies to "studying historical fiction for history" for one it's usually more interesting and studying people's take on something can be more educational than learning just the "facts" themselves.
My point is that you're not going to learn how schizophrenia develops, what the symptoms are, and how to treat it, from a random work of fiction that includes it. Sure, you can learn lots of philosophical stuff from analysing a story including it, and that tells you stuff about the author and the story, but it doesn't tell you how it works in reality.
You also cannot just dismiss reality or equate it to fictional works because we perceive it subjectively.