My dentist found that one side wasn't working as well as the other and made me a custom splint (a mouthguard I wear at night) which trains the weaker side to work properly. It looks like the one on the right in this picture [0]. Since then, all of the pains on that side of my neck and upper back have disappeared.
The way you've described your pain seems similar to what I was experiencing, so maybe this information gives you something to go on.
One caveat though: my dentist said that the mouthguard approach doesn't work for everyone (about 30% of people get a result similar to mine) as it relies on fooling your brain in your sleep to train one jaw muscle to be stronger than the other.
[0] https://healthyheroics.com/wp-content/uploads/2018/01/orthod...