The PS5 did initially let you transfer PT from your PS4 and play it on the new console. Until you couldn't. I know because I did it, and played it, on a PlayStation 5. However, if you try to repeat the process now you get the message during the transfer process that "you can't use this game or app on the PS5".
So what happened? It's unclear and I've asked both Sony and Konami for comment. So far Konami has responded asking that I "reach out to Sony about the matter", while Sony is currently looking into it. Whatever the outcome, the fact remains it was possible and now, for whatever reason, it no longer is. Here's a quick video showing the end of the data transfer which I initially did while setting up a review PS5 on October 27. As you can see the game copies over, appears on the main menu and then boots up and plays with no issue.
However, you might notice there's no sound. This was literally the first thing I tried on the PS5 and I think the sound was going to the headphones and not my capture gear. Rookie error. Not thinking anything of it, I deleted PT from the PS5 on November 1 to redo and recapture the transfer, with sound this time, only to get this:
The first thing to take away from this is that I had PT playable on a PS5 and I deleted it. It's barely a joke to say I've laid awake thinking about this. The second thing is: to wonder what happened? Konami has gone on record as saying PT won’t be backwards compatible with the PS5 via a PlayStation Store download, but the fact that I was able to transfer and play it initially suggests this may have been a conscious decision, rather than a lack of support. The option was possible and has been taken away.
Currently the game sits in my library marked as "Playable on PS4" and if I try to select it to redownload it (which isn't possible any more, I know) a message states that "This PS4 game isn't playable on PS5" and directs me to the link PlayStation.com/bc (opens in new tab). There you'll obviously find no mention of PT, beyond a footnote in the list of 10 games that are confirmed to be incompatible with PS5, saying that it "excludes demos".
For things that 100% will be playable on Sony's next-gen console, here are the upcoming PS5 games confirmed so far.