I have a fair amount of overlap with your problem.  Chronic mild-moderate lower back pain, 20 years or more, just put up with it; usually would feel better with weightlifting but occasionally worse, and standing for long periods would aggravate it.  Finally went to a PT (recommended to me but didn’t really cater to athletes) who diagnosed SI problem.  She could adjust it for temporary relief, but generally said to avoid activity that might aggravate it.  (She would describe my SI as “out”.)

I tried lots of the self-adjustments for SI you’ve probably seen on youtube, like the knee push/pull/squeeze and others.  Got temporary relief from some of them, but nothing would last.

I also had right adductor pain and often right TFL and hip flexor pain and tightness, especially after exercise, but my left SI was the problem.  I also discovered that my right knee was a bit valgus, and I’m still working on my right ankle mobility.

Found a chiro through a crossfit affiliate who mostly solved the problem through regular adjustments (maybe 20-25).  He described it as “locked” = not moving properly.  I had 4 months with almost no pain, away from chiro, but have fallen back into the same symptoms, especially after my last 2 heavy back squat workouts.  So I’ve been back for a few adjustments and the pain has quickly lessened.

Hope you get it solved.

Ed