Except that’s antithetical to what he was doing in the first place. He had zero need for an invisibility cloak to test himself out unless he wanted to see how easily he could ambush creatures when he’s already reasonably confident that he’s going into a dungeon that won’t far exceed his abilities. If he wanted to just test out how well he can one sidedly hit stuff while invisible he’d just have walked around during the daytime with the cloak on and smashed stuff Instead of waiting to break in after hours. He wanted a “real” battle so that he has a measuring stick and unless he exclusively uses the invisibility cloak normally (which he clearly doesn’t on account of the fact that he swapped it out) it has no use other than getting into the dungeon even more stealthily than he already was doing.
According to the chapter he said he has no intent of actually fighting cause of what he went through in the other world and just wanted to see the level that his summons are. His actual presence in the "real fight" as you put it had zero impact, which is doubled down on when his summon went buck wild in the dungeon.
Mind he didn't know that would happened either. But again either way, if his intention was to stand back and support his summons to gauge their strength, then it doesn't matter whether or not the monsters could see him or not. So ultimately in the battle it didn't matter what cloak he used, as he wasn't planning on directly participating.
And if it doesn't matter the cloak, it makes far more sense to use the more effective one if the cost to use them is the same. Maybe the invisibility cloak has a time limit, uses more mana, something. But its until its said they have different cost, they are the same cost to use.
Using the black cloak is like if one was to walk down the sidewalk just in your socks, rather than putting on sandals. Both have the same amount of effort, but one is clearly gonna work better in the situation.
The only reason I can think he may have used the black cloak is that maybe he wanted to be visible to his summons, but then that makes one ask does the cloak not work on them, and if that is not explained one could also assume that the invisibility cloak would not work on them. Most likely to master/summon bonds not explained at all.
This is all compounded by the fact that he wants to keep his summons and strength a secret, hence the stealth. Do you half ass being stealthy and secret keeping? That how you don't have secrets anymore, which is why we have this contrivance, its all part of the story. If he actually kept his secret he couldn't interact with the setting as much nor with the characters in the new world. And people would find that boring.
I mentioned this in my previous response, but I'll say it again. The only reason this black cloak exists is for the story reason of letting the MC show off his power in front of people despite him wanting to have a more peaceful life and keep his strength a secret.
Cause guess what, he'll do it again.
"Oh there is a sudden threat that no one can handle all of a sudden despite all these A Rankers around, better put on my black cloak and use the flashiest magic I can, then suffer cringe damage that people are talking about the black cloak again, so much so that I didn't go outside for almost a week."
That takes place by chapter 31 in the web novel (link
here if interested, its the jp wn as the translated one is only up to chapter six.)
If this doesn't make sense to you, then we will just have to agree to disagree, cause I won't be able to convince you and you won't be able to convince me.