Most of the points i would've made have already been covered by other individuals in a more fluent manner so I'll just stick to timestamping some moments and providing a bit of a conclusion at the end:
29:44- It looks like your situational awareness is off as your teammate gets pushed by a shotty player in the lane you cover, but you neglect to see him drop down on the staircase. You don't need to kill him outright as the position he dropped into favors his shotty more, but putting some shots into him before challenging top could have helped your teammate secure the kill and made the round overall less messy. That being said, the opening gambit you guys made was a good show of force and your tripmine usage was definitely on point.
30:43 - You're already a fairly slow class (laterally speaking) without using bones. Be aware that if you push with your teammates down the same lane, you need to match their pacing or you'll get locked behind by grenades and put them into a 2v3. In general, pushing top hallway as a hunter w/o bones is a bad idea because if this happens a better team will immediately collapse on your teammates before you even have time to go bottom or hop over the outside railing. Stick to bottom hallway unless the team makes you shake it up.
30:54 - Situational awareness again. You already know the angle of attack that player will take since he has to push the doorway. Don't get so focused on being ready for the ensuing fight you neglect to utilize cover. You fight him full in the open while he only has to push up a little bit from doorway (without ever even needing to give you any chance to hit him full exposure, his mistake there) to get a strong headglitch.
-Additionally, as you call out yourself, there are two enemies circling through your spawn and (potentially) about to push you. As long as you rotate to cover while still putting a presence on their radar, you could (again, potentially) isolate the third and collapse on them. At the very least, you could force them to push either of those hallways (disadvantages for them) or retreat to pool again, running the timer down.
31:26 - Good teams that are already skilled at making the right decisions under pressure can afford to play passively on maps with a large emphasis of control like asylum. However, playing passive is very different from a passive team playing scared. Round 1 showed me that your team definitely had enough area denial and placement to hold top, but only if you guys coordinate your pushes. Playing back at an angle that essentially leaves your hunter friend pushing top to die in a bad position does not help you to take top.
32:23 - Great tripmine here. You're right in that you pushed too slow to capitalize on your damage, but don't forget that the third player never took a hit, and for all intents and purposes baited you into recklessly pushing hallway. In those kinds of situations, avoid bottlenecking your approach. In fact, take a page from the other team's handbook and have someone put pressure from outside to muddle their focus on hallway.
33:26 - Playing pool is giving up. Trials gods can make anything work, but at your team's level, immediately realize that when you play passive you are giving up the game (that's not even taking in the fact that you were playing pool with a HC and a sidearm. At that range you should be helping your teammate in pool teamshoot with a scout or attacking from a different angle.
34:04 - Good plan, but bad pop. Heavy is basically a super in-and-of itself, so goldy should've been used down below to secure it for your team. As it is, popping the super outside just forced the enemy team to collapse on your team faster to try and avoid getting blasted.
34:21 - Map awareness, in addition to decision making. When you are last guardian and you need to make a play, you have to do your best to make a play. Maybe, at first, it won't be the right play to make, but the more you waffle in those scenarios the less time you have to try and turn what should be an absolute loss into a victory by the skin of your teeth. After locking that guy off with a tripmine, you should have made a beeline for the outside rez. Best case he accidentally walks into it and kills himself (what happened here), but worst case was he shoots or waits the mine out, picks up the rez in that corner, and then you have a potential 2v2 again with a guy who has self-rez ready and another guy who has heavy. Truth be told, rounds like that are already pretty decided, but you work with what you got, and you make the best of it.
35:27 - See before about the hunter and hallway thing. Push together.
35:50 - Hunter(s), hallway, you got punished. Try to remember what supers have been used and when. Good rule of thumb is 5 int supers should be up by round 3, tethers by round 4, and the best player's super tends to be the first you deal with in an average game. If you have it, play around with Perun for a few cards just to get in the "flow" of what supers are up when. Also, take note of the one teammate who talks (aside from you) in the vid. That's fairly important and I'll cover why at the end of this writeup.
36:57 - Your teammate should've been more clear about the rez down there.
37:53 - Great tripmine. Yes, you should've been more active with the goldy, as the player could've tried to 1-tap melee'd you while you went for it (He would've had the biggest balls I've ever seen if he did though, since he would've been banking on you not having a scuff and not being able to hit him first.) but since you still aimed in his general direction the rez wasn't as risky and it secured the kill in the end since you whiffed your shot (curious, are you running deadeye?).
Conclusion: Overall, you and your team suffer from what most teams suffer from in trials - Not being able to maintain aggressiveness in your decision making and positioning, Accidentally staggering your pushes and collapses (something you should eventually try to incorporate but only when you can successfully do it with intent), Accidentally baiting your teammates (again, a powerful option in your arsenal when you are skilled enough to utilize it properly), cracking under last-standing pressure, and not having a shotcaller (There were various moments I could hear through the comms where your other teammate fell apart not knowing what to do, and at the end rallied you guys to push top, confident the other team weren't skilled enough to challenge the approach. If not before the card, then definitely during it pays to have someone just put out a plan of action and be the leader. Regardless of whether they want the role or not, I guarantee you all want the win.).
A lot of these things will just come with practice (faster now that you know specifically what to look for), but it might help to run some funsies cards next week where your team commits to just being balls-to-the-wall aggressive (even if it means potentially dying, always pushing to help a teammate, pushing their last alive, basically getting as much exposure as you can to 3v3 teamshot chaos. Hopefully it helps you guys to understand how to play around each other better and develop synergy between you all.) and to take your team into skirmish a lot more. If you can, during the week have each member practice with only one other person (the last player on your team for skirmish/elim being a blueberry) until you've done a few games with each variant (so, 3 sets of games). This will help you both to rely on each other more, as you will basically be enacting single carries throughout the majority of those games. And, of course, the obligatory rumble practice. Ensure that every last bit of your gameplay can be aggressive if it needs to be, and more importantly IS always keeping your mind active. Hope these tips help.