"You can sovereignly host your own PDS" Yes. "... and entirely control your identity on bluesky" No. The PDS stores your data, but BlueSky maintains a central registry for IDs in their network. In theory, you could run your own ATProto ID registery. But from what I understand, it would be incompatible with BlueSky. It would be the equivalent of forking BitCoin to create your own blockchain. You can, but it doesn't allow you to transact over the BitCoin blockchain.
My understanding is that AT relays basically operate like a Nostr client does (obviously there's other differences in the protocol too tho). Even though another AT relay couldn't interact with Bluesky, it could pull from the same PDSs so people would be able to interact - just like how Nostr clients don't directly interact, but we're speaking since our clients are connected via relays.