I tried to search for it in Google, and asked AI, but yet I didn't understand.

I mean, if you go to the front page, you see some games show like #hashtags between the author name and the description, but these don't always match the game tags. Where do these #tags come from?

but these don't always match the game tags

You sure about that?

The games on the front page you talk about are in the segment of featured games. That list is curated. Which means a human put them in that list and very likely selected some hash tags. And those hash tags link to itch tags, so they are probably tags of those games. But developers can change tags later and humans can make errors and link the wrong tags (or disagree with the tags the developer chose).

So I assume games that have those hash tags are either currently in the featured list, or were curated in some other way. And only the front page will show such hash tag tags.