I've seen the same issue mentioned in the Resolved Issues section of the Japanese forums.
https://forum.square-enix.com/ffxiv/threads/510798

Here are the translations. The menu names might be different. It looks like the second method is simpler.
On your PS4 console, go to the home screen: Settings → System Browser → Options → Settings
Select both Delete Cookies and Clear Website Data
I also occasionally experience cases where the ID, password, and one-time password input fields do not appear. In such cases, I open any topic within the launcher and then go back — which, for the PS4 version, effectively acts as a "reload" — to make the input fields appear.