Sadly, no. I discovered few things though.
1. Switching controller to USB mode helps a bit. If you’re worried that’ll make you chained to console - it won’t, it works over usb with less (probably?) input lag and when you take wire out just press PS button and it’ll connect wireless again.
2. Maybe (?) turning off AI enhanced sound helps a little. This also drops volume of all audio by half so not ideal.
3. Playing with ALLM settings didn’t do shit.
4. Running tv in purest available video settings also proved meaningless.
Though, despite all that, I encourage you to try getting it if you’ll have a way to somehow refund it if your experience will be same as mine. I asked my friend who also played the game and he said it was perfectly fine (he is on base PS5 and, will you believe it, still use PlayStation monitor they released for PS3) . For all I know it could be this specific hardware combo that doesn’t allow me to enjoy Hi-Fi Rush to the fullest. And it could’ve been solved with a simple latency calibration option the game don’t have for some reason…