I agree with all of this but just to add, the pain can indeed be a real physical issue directly caused by mental health.

For example, anxiety often causes muscle tension and bad posture which can lead to real mechanical pain causing issues. I suffer from panic attacks and they are a very physical experience. My temperature stops regulating itself properly and I get GI problems. This is likely an indirect consequence of the adrenaline surge, but there are other known and theorised ways that your mental state can influence your body.