Need help with bone constraints

https://reddit.com/link/1isnpth/video/hdpj937gpyje1/player

I'm attempting to make a robot dog with a top-mounted arm that has a rail for weapon attachments. It is for a game. The base of the arm obviously can't rotate in any direction but Z without clipping into the body (or looking stupid), but when I add a rotation constraint and limit the x axis, it adjusts the bone's position and introduces some funky movement. What should I do to fix this? There is an IK bone on this arm, for context. In addition, is there anything else I need to do for the rest of the chain of limbs for the arm? The legs are working as expected, but I'm not sure what, if any, additional steps I should take to ensure the arm looks right once the base's rotation issue is remedied. Thank you!