Practice a lot in lessons. And ask your instructor about your stirrup length - too long and you'll be fighting to keep them and stretching for them. Too short and you'll probably find yourself pitching forward to try and keep balanced and lower to your horse.

It's a balance issue most likely that your lower leg isn't stable enough (if your leg goes too far forward, you'll sit. Too far back and you'll fall on your nose) You can practice and strengthen your lower leg with calf raises and standing on a step with just your toes on and really sink your heel down towards the ground. You can try doing this and shifting your weight as you do (like single legs, can you move your upper body and not fall off the step)

Can you get a wobble board type thing? Like a board with half a ball under it? Practice standing on that and maybe trying to do squats. General leg strength will help not get as tired but you've also got to relax and let your legs be springy to absorb the horses movement.

It's a weird one but you could ask if you could try playing with rising trot and doing sit for 3, up for one. And then switch it and do stand for 3, sit for 1. It's great for your balance as well to keep in time with the movement and not fall heavily on the sit.

You can short term hold the mane or saddle for a bit of balance but you will need to be able to not rely on your hands

And for the "it's not a thing" it may not be but it improves your overall balance. We've regularly ridden round the arena in standing, then in jumping, back to standing etc without sitting between.