If I buy the game on one platform, can I continue play it on any platform?

Once you hit rank 25 in the free trial edition of Knockout City, you’re forced to buy the normal or deluxe edition of the game to continue playing. This is fine, but since I want to play on a few platforms I’d like to know if buying the game on any platform will give me unlimited access on all platforms. Otherwise I’ll have to pick the one I want access to the most right now.

During the block party trial period, the game featured cross-progression between platforms.