I'm also having this issue. It's really strange. I've tried the troubleshooting mentioned above, and I've even gone so far as to completely uninstall, then reinstall the game. I've tested my controller and it works fine, tried with other controllers, still not able to sprint properly.
It's bad enough that I am unable to progress in the game. I'm at the part where there's a big centrifuge that you have to get past by sprinting (also confirmed online that this is the correct solution). I'm really enjoying it so it sucks to be stuck after already spending several hours playing ☹️
I would be willing to submit a bug report or something but I'm really not sure how that works on a PS5. I usually play PC
Any assistance would be greatly appreciated