Just finishing going through this.
Your army composition seems good and you generally make good decisions. You're clearly winning early game and half the time I suspected you'd uploaded a replay where you won.
I've identified a few issues that cost you the game, and the good news is they're easy to fix.
Squad Clumping
When you're up against any sort of AoE or suppression you need to separate your squads. There were several times you got two squads suppressed at once by an enemy HMG because they were too close together. This also hurt you against the Centaur.
Sniper
I suspect this was a misclick but just in case never move the sniper in front of the rest of your forces unless you're directly microing it. There should always be another squad in front of it.
Machine Gun Attack Move
Ideally you usually shouldn't send an HMG into the fog of war without support but when you do issue it an Attack Move command, then shift queue the setup position you want. This means if it spots an enemy unit it'll set up and fire from maximum range, either suppressing the enemy unit or giving you a good chance to safely retreat it. You lost two HMGs because they walked into enemy fire and kept walking until they were dead.
It's also a good idea to do this with infantry when you send them on capping missions you're not focusing on.
Cover
You have a tendency to leave your squads out in the open when they're holding a position, even when there's green cover right next to them. There was one point where you had two squads guarding a point in red cover. Green cover grants suppression resistance, halved received accuracy and halved damage. Unless you're facing a lot of AoE it's usually best to stick to cover wherever possible.
Skillplanes
Treat a skillplane strike like a very powerful, very long artillery strike. Get out of its radius as fast as you can and wait for it to pass. Both times your opponent deployed skillplanes on the central point you stayed and fought, meaning the skillplanes slaughtered your team weapons. When your opponent uses skillplanes they claim that area for a bit. Whether they claim it because all your units ran away or because all your units died is up to you.
Concentrate Fire
This is a fairly small thing but I noticed in one of the armour engagements you had your PaK shooting the Churchill and your Panther shooting the Centaur. If you'd had both firing on the same tank you'd have managed to knock one out.
Team Weapons
I'd say the main reason you lost this game is because you were too passive with your team weapons. Don't be afraid to be more aggressive with them. There were several infantry fights you lost when you had a friendly HMG just behind you you could have moved up to support. Your mortar was a good build choice but you left it in the corner of the map where it couldn't contribute.
This goes most of all for the PaK guns. His defensive position was two tanks covered by two AT guns. Those two AT guns prevent you from driving your Panther up there but you could easily have crept forward with the PaKs. Support them with your HMG and mortar, keep the Panther behind them and there'd be little he could have done apart from throwing down the skillplanes. If he does that pull back, wait for the skillplanes to expire and attack again.
Summary
Your play is pretty good. Things to improve based on this are avoid bunching your squads up, use green cover when it's available, be more aggressive with your team weapons and don't try to tank a skillplane attack.
Thank you for reviewing the replay and giving advice. I will upload another replay against the same player where I lost aswell. I think he just outnumbers me tank wise and I crumble.
If you want to analyze the next replay I would appreciate it.