The game is locked to 60FPS in-game, which AMD overlay confirms. I have tried all different graphics options, but none seem to enable a higher framerate than 60. The game does identify my screen with the correct refresh rate (165hz), which I have selected in-game.

Normally I use linux, but I confirmed the same issue is there in Windows 11. So the issue seems not OS-specific as well.
Other specs:
Ryzen 7 5800X3D / RX 6950XT, 32GB RAM, NVME SSD
GOG version of the game (as of 4th May fully up to date)

Anyone knows how to make the game use higher framerates?

Its possible that it maxes out at 60. Not every game allows for unlocked or higher fps.

If you can get it lower by forcing something like say 30 fps limit in GPU driver software then its probably limited to 60. I haven't looked into it.