Who needs a gym? Just put your bag on and do squats. Deadlift a 2U server. Improvise.

you don't need a gym for core strength

literally do pull-ups with bicycle kicks. if you also rotate the bicycle kicks so your legs so to the left or right side of you it'll increase the amount of energy you're using giving better results.

it's hard... but gets easier. strength>bigger muscles.

example video - https://m.youtube.com/watch?v=gR1vUVuKyxA

I have a little incline bench and some adjustable dumbbells, that and my body weight (on a yoga mat for dead bugs and glute bridges) have been getting me in shape. You can do a lot of exercises with just that small investment and space commitment. Definitely do the core and back workouts you need (I used to have chronic upper back pain too).

I found this really helpful, and you can do it at home.

https://media.ccc.de/v/gpn20-90-rckengesundheit-fr-nerds

The lecture is in German, but you can still see the exercises.