I'm on Windows 11. I found the gamecontrollerdb.txt file already and took a peek (ctrl-f) and it does have multiple entries for PS5 controllers. The game literally says "PS5 controller detected" so I don't think the problem is that file.
While writing this I decided to try again for fun, and the first time the controller was working so I was about to delete the whole thread. But then I quit the game and tried again and the controller isn't working anymore (one time it let me do a single down input and then stopped). When I get to this state I can still unplug and plug back in the controller to get the connected/disconnected message, but there's still no input. I quit and tried again a few more times after this but it's still broken whether the controller is connected before the game starts or after. I'll let you know if I can figure out a better way to reproduce the problem.