The official Sea of Thieves website has confirmed in a Q&A regarding the upcoming PS5 release that the game will run at 120 FPS for Sony's console, matching the Xbox Series X version of the pirate adventurer. Furthermore, Cross-Play is also officially confirmed, but you can turn it off if you want.
Sea of Thieves on PlayStation 5 is optimised to run at 60 FPS in 4K resolution, with an additional performance mode available for supported TVs allowing for 120Hz refresh rates at 1080p resolution. This has parity with the Xbox Series X experience.