Launcher to change graphic settings doesn't work, to solve this you have to add this lines to edit.reg located in Home/.local/share/steam/steamapps/compatdata/ XXXYourGameNumberXXX/pfx (Values in HEX)

[Software\Ubisoft\Prince of Persia\1.0\Engine] 1704251529 #time=1da3df2a39bd6d8 "AlternateVerticalSync"=dword:00000001 "AlternateVerticalSyncThreshold"=dword:00000000 "Antialiasing"=dword:00000002 "AspectRatioOverride"=dword:000000a0 "DegradedTextures"=dword:00000000 "LNG_Language"=dword:00000001 "ParticleEffectNumber"=dword:00000064 "PostEffects"=dword:00000002 "ScreenResolutionHeight"=dword:00000320 "ScreenResolutionWidth"=dword:00000500 "Shadows"=dword:00000002 "VerticalSync"=dword:00000001

[Software\Ubisoft\Prince of Persia\1.0\Launcher] 1704251530 #time=1da3df2a3ff99de "AspectRatioOverrideCHKB"=dword:00000000 "DefaultSetting"=dword:00000001 "LauncherVersion"=dword:00000004 "LNG_Language"=dword:00000001 "Texture_lvl"=dword:00000001 "VerticalSync_lvl"=dw

I tried the Steam version first but could't enjoy the game without analog controller support. I ended up installing the gog version of the game with Lutris but I assume it would work the same using Heroic Luncher with the same tinkering to change resolution.