Short Answer
No. Crimson Desert does not support cross-save or cross-progression between platforms. Save data created on one platform cannot be transferred to another. Pearl Abyss confirmed this in the official pre-launch FAQ.
What This Means
If you start a playthrough on PlayStation 5, you cannot continue that save file on PC or Xbox Series X|S (and vice versa). Each platform maintains completely separate save data. There is no Pearl Abyss account system that syncs progress across devices.
Xbox Play Anywhere Exception
There is one limited exception. If you purchase Crimson Desert through the Xbox Store, the game qualifies for Xbox Play Anywhere. This means a single purchase grants access on both Xbox consoles and PC (via the Xbox/Microsoft Store app), and save data syncs between those two platforms. This does not extend to Steam, Epic Games Store, or PlayStation.
No Crossplay Either
Since Crimson Desert launched as a single-player game, crossplay is not applicable. If a multiplayer mode is added in the future, Pearl Abyss has not announced whether it would support cross-platform play.