I first wrecked my back 25 years ago, and not being insured, had to heal myself. Along the way I learned a few things.
First one is the biggie. Your back is telling you what works and what does not. I was truly amazed to find some people need to bend a little, and some a lot, to be comfortable. You gotta do what works for you. Your back will very quickly tell you what it does not like.
My injury, and most I have heard of, responds best to the standing at attention position, sitting or standing. As if I had a stout brace on. Wore one for a time, till I got stronger muscles around my kidneys. My injury means if my muscles don't lift my lower back up, my L3 disk will twist 10 degrees, and then it grinds on nerves. I can flex muscles and hyperextend my back in nearly any position, but it still works best in straight up, or lying down posture. For this reason, I need a very upright position on a bike, to ride for more than one hour. I sit very tall in a car seat too, for any kind of long drive. I can't tilt that seat back way back like I liked when I was young.
When I started e bike commuting, I was spending two hours a day on the bike, and quickly found I needed a tall seat, for too low would start putting a lot of strain on the knees. Then the bars were too low, so I went to bmx bars that had a lot of rise. All this also on full suspension bikes, which also helped reduce the shock on my lower back, letting my back muscles not have to work quite as hard. These bikes were teen size cheap bikes that did not fit my long legs, so the fit was poor from the get go. Later, I upgraded my bike to a more adult size, and could go back to a bmx bar, but one with some rise in it. Then even later, I got into long tail bikes. Really, even without a back injury, a proper long bike helps a lot. On traditional bikes, the seat is too close to being over the rear wheel, and all the bumps go right up the seatpost. The seat is constantly jarring nearly straight up unless the bike has rear suspension. But on the longtail, the seat is nearly centered between the two wheel axles. On a bump, the front wheel goes up, and the saddle merely rocks back. This is true on any bike. Then on longtails, when the rear wheel hits that bump, it just rocks the saddle forward. No jarring of the spine. Sure, you will still feel a big pothole, but road cracks just gently rock the saddle back and forth, instead of jarring your ass up and down 3 inches.
Bottom line, find the bike that works with your particular back issue, and work on your core strength. I used to hang from a chin up bar and just do crunches. It was as good for my back as a hundred buck trip to the chiropractor. As for the bike, try everything. Some swear by recumbents, and I get that idea too. But the bent just does not do my back any good, for me, standing tall on the pedals still works best, with my ass only barely sitting on the saddle. By pedaling, I keep little of my weight on the actual saddle. You will likely need something different, just find what works good for you.