itch.io doesn't have a large enough team to go through every project and ensure it is using the correct tags
Tags are not ensured by itch staff at all. And there is no such thing as correct tags. To elaborate: for any given game you could "correctly" apply more than the allowed 10 tags, so how would you rank the tags to get a "correct" 10 tag combination. Steam seems to do it by popular vote of the players.
You might complain about blantantly and misleading tags with the report button, but I believe that is more for music categorized as games or for obvious tag spamming. Most of tag usage is in the eye of the beholder, and the one selecting the tags is the devs and they will have different opinions than many users.
I bet I would not even tag half the "horror" games here as horror.
Projects are not immediately indexed
While search and browse are affect from not being indexed, I was talking about search. Browse is not search. If you select a tag in browse you will see all available items indexed with that tag, with a dubious popular ranking that is not really accuratly reflecting popularity. Or rather, they do not tell how they calculate and how they define popularity. There is random in it and boosts/weighting for new/random stuff despite there being a separate new&popular page.
So to say it again: if you use search you will not see all matching results. What you get is truncated and randomized. So yes, there were complaints about indexed games not showing up in search. There is no guarantee to show up in search, even for a specialized search term.
Just try searching for horror (not tag horror, entering horror into the search box). Currently there are 72 results, despite there being 44000 games with the tag horror. To make it more complicated, just because you tag horror does not mean you will show up with a search for horror. You need also mention "horror" in the game description, better in the name of the game, at the very least. The search algorithm does not look at tags.
For example, I can currently find your "cottage cats", but not the "monster girls" assets. Despite using partial title match search term and only 28 results showing up for the monsters and 60 for cats.