it's unfortunate that "adult" seems to be considered to just mean "pornographic"
In the US? Yes. Read here https://en.wikipedia.org/wiki/Entertainment_Software_Rating_Board#Ratings
There are so few games that have AO, adults only, that they made a list. And you can count the games on that list that are not of a lewd nature on one hand.
To go above M17+ with non lewd things is near impossible. So adult game is a synonym for certain content - just like in "adult book store" or "adult toys".
I also would wish for more content granularity to filter. Age is so one dimensionally.
And then there are games like Darkest Dungeon. Look at the official ratings. It has T in the US and even in restrictive Germany it has 12+. If you do not know Darkest Dungon, I suggest you have a look. And then compare any of your planned "mature" content with the content of that game.
I think as adults we tend to lump children together. Teenagers are technically children in a legal sense if used as a synonym for minors, but actually, the phase of being a child only goes from birth to puberty. A game not being 18+ does not mean, it is family friendly. And Itch is intended for 13+. Unlike that Scratch gaming site, which is intended for 8-16 and even has a ScratchJr for 5-7 yo.