Just a thought, but as well as a new 🏍 have you thought about core exercise and stretching?
I had/have a bulged disc or two that cause me issues. If I haven’t stretched off properly before riding, my lower back gradually tightens up until it hurts.
A good set of stretching before I start looks a bit stupid but makes the ride so much nicer.
Glute bridges done properly on a regular basis also really help. I’ve slacked on those recently and starting doing some runs and I’m struggling with my lower back. Started up on the bridges again to balance / strengthen my core.
I do find the hardtail is worse for my back than the fs though. So the hardtail is for playing and short hard pedally rides – the big fs for everything else.