Personally I never had any results from home workouts because I just can’t get into the mindset; you always have the possibility of stopping mid-workout. At a gym or other dedicated space, once you’re there you figure as long as you made the trip you should stay and finish up. But your mileage may vary.

It’s also difficult to overload when you’re limited in the weights you have at home, and the lack of equipment prevents some very interesting exercises, like the back hyperextension on the purposely made bench:

I don’t know you personally but I still agree with your doctors, it sounds like your problems could be solved with exercise. It’s good that you have this confirmation at least, it tells us you have options.

I have slight scoliosis and my lower back also hurt sometimes, but now that I’m fitter, my lumbar muscles help keep the spine in place and I have completely stopped feeling any pain in my lower back. Same thing for the tendons, I expect you spend hours on the computer, like most people these days, which means your arms are always bent and your tendons become soft.

For the back problems you normally would look at weighted back exercises that target the location of your pain. Your back is all muscle but essentially there’s the shoulderblades, upper back, and lower back.

For the tendons, this is fixed with exercises that work your tendons indirectly, like the bench press: most of the weight will go into your chest, shoulders and arms, and your tendons should be spared. They will then slowly reinforce. You should find an exercise that doesn’t hurt your tendons (personally I had better luck with barbell exercises than dumbbell exercises when I had my tendinitis), and you should also stretch your tendons throughout the day:

(do both: palm facing out, palm facing in, both arms, throughout the day).

Is it possible for you to visit the gym on your commute? E.g. leave work -> go to gym -> go home? How about other facilities, like a pool?

I’m of the opinion that you really can’t beat resistance training, muscles are the basis of a healthy life and transfer to everything you do – the cliche of the bodybuilder who can’t touch his toes is exactly a cliche. But there’s a low-impact cardio exercise you can do at home if you get a rowing machine

They’re super expensive and you only do a pulling motion, which means no pushing muscles will be involved. But it could be a solution if you want to train at home. There’s other cardio machines of course, like treadmills or bikes, at varying price ranges but I like to recommend the rower because it works your whole body and is low-impact.

Also check out this guide: https://en.prolewiki.org/wiki/Essay:A_nutrition_and_fitness_guide. You can start working on your weight or physical fitness independently of the other.