Totally possible. Short version: Buy the keys for the new version you want access to(PC to PS4/5 or vice versa). Apply them to the same account, and make sure that is the account you are using to access the game from the second platform. Then when you buy expansions either get both versions, or get the version you want to have access to the newest content on. If for instance you only got the starter edition on PS5 but have complete on PC, then you would only be able to do starter content on the PS5. If you accidently logged off in a complete edition area, you wouldnt have access to the character on the other console. Though, this can also work in your favor if you think you would only want to do more chill content(gold saucer, etc) in bed then you could save on the version you get. Or you just wait for a good sale, and get everything.

SirCadogan - The two versions that arent compatible with each other are the PC version, and the PC(steam) version. Whichever version you get first on your PC is the only one your account can use, and also becomes the only source you can use for upgrades(steam expansions arent valid for non-steam accounts, and vice versa). Thus most people are encouraged to get the non-steam version, if only because its easier to find sales when you arent stuck with steam as your only vendor.