New player here :)

[Niwashi]

The MogStation will remain where you access your subscription (and pay subscription fees once your free period ends), but it's only the PC and Mac versions that you register there. The PS4 version is registered to your PSN account (which happened automatically if you bought it through PSN) and then your PSN account is linked to your Square Enix - FFXIV account.

The first time you open the game on PS4, it asks if you already have a Square Enix account or want to create one. If you create a new one, it will be completely separate, without access the characters you created on PC, and will require its own separate subscription as well.

Or instead, you can tell it you already have an SE account, log into that, and confirm that you want to link the two together. That way both platforms have access to the same characters, and both share just a single subscription (though expansions would have to be purchased separately for each once you get to that point). The only downside, if you consider it one, is that you would be unable to log into the game on both PS4 and PC at the same time.

So, if the PS4 version is so that you can play with a family member or dual box with both platforms at once, then create a new account for it. If it's so that you have a choice in which platform to play your main character on, then don't. Once a new account is created, they cannot be merged together. And once your PSN account is linked to a SE account, it cannot be changed to allow that PSN account to use a different SE account. (You could create a PSN sub-account and link it to a different SE account, but it wouldn't have the game you purchased from the PSN store, since that copy was automatically registered to the PSN account you bought it through).