Other users can't change search visibility, only the itch.io staff can, so your open support ticket is the right place for this. Since you already have ticket 408860, I'd avoid opening duplicate tickets, as that usually doesn't speed things up. In the meantime your game page and its direct link should keep working, so you can still share that link with people. Replies about indexing can take a while, so some patience is probably needed. Hope it gets sorted out soon, and good luck with the next release.
The thing is, I once had a situation where one of my games dropped out of the search index following an update, due to a false positive. I understand that these things happen.
I reached out to the administration first, and then to a moderator. Posting here definitely helped speed up the process.
With that in mind, I’m hoping a moderator will take a look at this thread.