As I understand it, it ingests an uploaded video and automatically encodes it in a bunch of different quality settings in h.264, then, if the video is popular enough to justify the computational cost of encoding into AV1 and VP9, they'll do that when the video reaches something like 1000 views. And yes, once encoded they just keep the copies so that it doesn't have to be done again.

Here's a 2-year-old blog post where YouTube describes some of the technical challenges.

As that blog post explains, when you're running a service that ingests 500 hours of user submitted video every minute, you'll need to handle that task differently than how, for example, Netflix does (with way more video minutes being served, but a comparatively tiny amount of original video content to encode, where bandwidth efficiency becomes far more important than encoding computational efficiency).