Oh dang if it bothers you all night you’ve got some more severe dysfunction. If it is a new bed that helps then you presumably feel relief from greater firmness. Are the mattress toppers firmer than the bed or softer foam?

Though really, a physiotherapist will be the best kind of person to talk to, still assuming it’s muscular. You’d want to identify which muscles are causing the pain and then do exercises and stretches that will help them be less tight. Tightness can come from compression or tension, so the exercises to do will vary by muscle.

Some examples. If your psoas is tight, it will be tight in compression and need to be elongated. If your lower back muscles are doing extra work because your lower abdominals are weak, you’ll want to do core strengthening exercises. If your upper back and neck hurt, it may be from slouching, which usually calls for strengthening your upper back (pull ups, presses, pull downs, etc). A PT will be able to guide you in propee form and better identify the issues.

In the meantime, have you tried heat on your back? Like a heating pad? This can often relax muscles. Also, do you massage your back? This can actually make things worse.