Update:
I have a decent home gym with lots of options (squat rack, treadmill, deadlift platform, spin bike, bench press) and stopped cycling altogether (spin bike or on trails) and my constant back pain disappeared. For the second time since I stopped training/racing, I started working out on the spin bike, and for the second time my back started hurting again.
I really enjoy spinning as it's kind of a mindless workout where I can browse on my phone or watch a movie and get cardio in. I can't really do that on a treadmill as easily.
So, yeah, it's the bike that's causing my back pain. I'm going to see if I can raise the bars even higher such that I can sit completely upright and see if that solves the problem.
No joke, going for a vertical back like this:
