It has been several weeks since I published my game, but it looks like it isn't indexed yet
It depends. Your game was flagged by a bot in the mean time, so you might have to contact support. And I mean the rules you were shown before being allowed to post here. You had to tick a checkbox labeled "I've read the rules" before being allowed to click Post. By the way, those rules include not asking how long it takes.
Your account is two weeks old.
Indexing can take several weeks. And you have payment active. That takes extra time.
The other account is four weeks old. Also payment active.
It takes time, people. Itch is free. It is holiday season. I would imagine that some staff is on vacation and the people that do work have lots to do.
So the answer to this and all the other questions (why is my game not indexed) is usually: Because it is in a queue and the queue waiting time can be weeks.
Oh, and the game from this topic was indexed in the meantime.
The faq should really be updated. It still talks about the time to be days, instead of weeks. Telling people to contact support after a day is not helping here! It clogs up support with unneccessary support requests, and since there are no answers to those requests, people create topics here.
https://itch.io/docs/creators/getting-indexed#why-isnt-my-project-showing-up
(The game is indexed now, so 4 weeks it can be.)