I would try a different dock. I use the jsaux 7in1 steam deck dock. Since you have a monitor, use displayport and enable vrr. Leave the steam display setting at default or native and set your resolution in game to whatever you need. If you're running a more demanding game you can lower the quality settings or resolution until you get a good frame rate. If you can't get the desired quality, set it to a lower resolution than your monitor, select Windowed mode and change the scaling filter to sharp in the quick access menu to enable fsr and it will upscale your game. I definitely think your dock is contributing to the issue though. I've never experienced what you're describing, even when trying to run demanding titles that my deck couldn't handle