Ok, how's your flexibility? Some low back mobility issues are causes by tight hamstrings and glutes.

Check out r/flexibility for that stuff, there's some good info there.

For weightloss you're gonna have to be in an energy deficit (burn more calories than you eat). This doesn't mean you have to do a shit load of cardio, you can't out train a bad diet, it does mean you'll have to restrict calorie intake. Look up Jeff Nippards videos on YT, he has videos on nutrition, losing fat, gaining muscle, etc. This also doesn't mean you have to go hungry, you'll just have to eat less calorically dense foods and will want to maintain protein for muscle gains.

When my low back sucked I started with 45 degree back extensions. Start with some low volume.

Try say 3x8, no weight and do that twice a week for 2 weeks and then do 3x10 for two weeks and then 4x10, and then go back to 3x8 and hold a 10 lbs plate, then back up on sets and reps adding weight over time. (this is just an example you can apply progressive overload in different ways).

There are lots of different ways to train mid and upper back (lats, rhomboids, traps, teres major and minor, etc. (deadlifts, lat pulldowns, lots of different Row variations, shrugs, etc).

Fat loss will happen way faster than muscle gains, it's a marathon not a sprint, so don't get discouraged.

You're probably tight from being sedentary, stretching and mobility will make you feel alot better overall so definitely program that.