But what if the post I'm searching for is not on lemmy.world? Say the instance doesn't even have Lemmy in their name, like beehaw.org. How would a search engine index it? How would it know it's part of Lemmy?

Interesting. I hadn't even thought about how the fact that instance1.[post] and instance2.[post@instance1] is essentially the same thing and how search engines would handle it. Interested in what you come up with!

So we were aware they weren't completely extinct since we were keeping a few around? The title makes it seem like it just popped up and was a complete surprise.

I imagine that would be quite inconvenient... Especially as Lemmy grows and has potentially many more instances.

You should look into ReVanced :)