Hey all, this is correct indeed. BF2042 supports cross-progression between the various console generations and PC. But also please be aware of the following:
CROSS-PROGRESSION
As a reminder, we also have cross-progression functionality within Battlefield 2042, which will be shared across all platforms and travel with you wherever you go as long as you play on the same EA account. This means your unlocked progress and completed purchases in your PlayStation® copy of the game will carry over onto the Xbox or PC version, and vice versa.
For example, your new unlocked skin for your M5A3 assault rifle on PlayStation®, alongside your in-game progress such as Player Level and Mastery, carries with you if you now choose to jump into the action on Xbox Series X|S.
While there are a few limitations to cross-progression we want to make you aware of, such as Special Edition cosmetics, the Digital Artbook & Soundtrack, unspent Premium Currency and pre-order items not carrying over, we’re excited about giving you the freedom to play and progress wherever you choose to play.
From our website: https://www.ea.com/games/battlefield/battlefield-2042/news/battlefield-briefing-progression-and-cosmetics