Yes the PS4 and PS5 versions are separate installations. You can continue playing the PS4 version on PS5 along with playing the PS5 version if you choose to download/install the upgrade on the PS store. When you're hovering the game's icon you can press the three dots to go into the PS Store to download the upgrade.
Might have to restart the game it was buggy for me when it came to the camera. Just move the camera around the evidence and/or move back a bit until it says "target in view", otherwise it won't register.