How are you getting that? On my Sony x900e my Pro shows up as PlayStation 4 in the Bravia Sync menu
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PS4 was released in 2014. PS3 support was dropped from FFXIV in 2018. Even if PS5 is released this year as some of the more optimistic estimates claim, it'll likely take several years until PS4 support is dropped. It looks like about half the player base is on PS4 so it would be financial suicide for SE to drop PS4 support as soon as PS5 is released, because not everyone is going to upgrade their consoles immediately.
If they dont plan on updating the graphics engine I dont think the PS4 version will get discontinued any time soon even 3 years after ps5 releases.
It would be extremely shocking if the PS5 was not 100% fully backwards compatible for PS4 games. So, yeah, XIV will be available on PS5 from day 1.
I expect FFXIV to be a launch title and possibly a showcase title.
With both using X86 based CPU. The port should be easier. However I don't think we will see it on ps5 for atleast a year + after release and who know the state of FFXIV in 2 more years.