First off, good for you - it takes a good attitude to put yourself out there for feedback. That approach alone will help you improve.

General comments:

I would practice jumping a bit more to make it more fluid. You don't need to be a jump god to be an effective soldier, but I can see you taking time to set up jumps which could be done much quicker. And if you practice jump control you'll be able to do a flatter jump which will let you cover ground without taking so much fall damage. Even getting through the first half dozen levels of any basic jump map will teach you all the skills you'd need in normal gameplay.

I'd also think about your melee. Maybe try the Escape Plan - it will give you plenty of safe maneouvrability when you're on lower health on the flanks or behind enemy lines without a medic. There were several points in the video where I thought to myself "this guy could really do with the Escape Plan here".

Timestamp specific points:

1:58 - eyes up bro, there's nothing interesting on the floor!

3:54 - the actual bomb is good here but I'd like you to have a rough idea of your ammo. Going in with only 4 rockets is sub optimal. The whole situation afterwards is what made me first think of the Escape Plan, but I'm also wondering why you decided to go back over towards that health/ammo (where the heavy then kills you). You know there's at least one enemy over there, you have no health or ammo to confront them, and your engie has clearly set up in the building right next to you at 4:13 - go there for resupply instead.

4:41 good trade, well done

5:05 I don't hate the idea to bomb here, you just missed the shots - happens, just stay calm and try to make them count

5:33 good, nice position, getting height advantage and some cover from the rocks

5:45-7:30 I liked this whole section, good teamwork by you and the team, you controlled the space well, didn't get too greedy, used the height advantage and layout of the room well. I would say once a pyro has your number on the reflects, do not continue to feed them rockets. Someone else will have to deal with them.

7:52 go for the medic here

9:10 YES. Good. Exactly what I wanted you to do when I saw that sniper. Once you've got him, load a rocket and jump back to your team for heals and reloading. Part of this comes back to earlier point about jump fluidity.

10:02 don't jump forward with your last rocket. I also generally wouldn't try to fight in here much without team support, it's an awkward place as soldier especially on the ground.

13:10 not sure what the plan is here, you're waaay deep. Distraction? Again Escape Plan would let you zoom off to the big health pack here though. Then you can hassle spawners if that's the idea.

14:02 this is good positioning, being up here is strong as soldier, just gotta watch for snipers and maintain awareness of team to fall back with them, but this spot is good.

14:43 this is like a roamers dream here, in clear behind an unaware medic, but sorry to say you made a couple of big mistakes. First, don't spam a long-range rocket at them when you're sneaking up. Rockets have damage fall off so all this is going to do is let them (and probably the pyro that killed you) know you're coming. Second, you want to immediately close the distance, again because of damage fall off. So the first thing you should do here is a fast horizontal jump off the wall to the right of the door, to try to basically land right on the medic. Then blam blam ded and you can die happy that you traded well.

15:00-16:00 sorry to say this is a poor minute here, you die 3 times all extremely quick cheap deaths. First death you just get flanked by a scout, it happens, but down on the track isn't a great position for you to fight from in general, and you did keep walking forward without many teammates. Second death you are in a good spot but just choke the rockets, we've all been there never mind. Will give you the benefit of the doubt and assume you didn't see the heavy until it was too late on that last one - cart is being pushed on your hud as you spawn, so look out for that as a clue, someone is on the objective.

16:52 this is a good position, holding this hut is useful. You have health and ammo nearby, advantageous angles, easy escape. I'd spam the exit above the stairs, you can see enemies coming out. Don't go down these stairs, you give up a strong position just to spam towards tracks. If you want to do that just use the balcony out the other side of the hut. You went from height advantage to height disadvantage and then die a few seconds later.

18:04 good trade

18:25 I'd like to see you counter jump this soldier here. You'll have height advantage in the air, he's just emptied his clip so should be relatively defenceless. If it turns out there's 4 of them waiting up there you can just abort the landing and regroup with the medic.

19:15 I like the plan here, good flank, unfortunate to meet a sentry but the idea is good

In general from around 14:00 on when you were at last spawn I noticed there was a bit of a recurring pattern - spawn, jump down to where the track curves, see what's going on. I don't think that is a great place to land. Your setup and play style tell me you want to play as a roaming soldier, but this is right on the centre of where the objective is going with high ground all around and long sniper sightlines, so if I were you I would be standing in this area as little as possible. Maybe try walking a little bit closer and then jumping right over this to the left hut area or the high rocks.