You can play the PS4 version on your PS5 (I'm pretty sure; they said most games will be backwards compatible, and I haven't got a PS5 to test if Nioh is or not) - but the free upgrade to PS5 is only for Nioh 2. For the PS5 remaster, you have to buy Nioh again (but not Nioh 2)
But there is crossplay. In fact, I just got patch 1.23 for the game - the one that enables crossplay.
But your save file will transfer - there's an added feature in both Nioh and Nioh 2 that allows you to upload/download your save to switch between PS4 and PS5.
The definition of insanity is doing the same thing again and again, while expecting different results. (As defined by Einstein)
Maybe we're all a little crazy.