Really, the base thing is that you are criminally not pressing things on CD. It looks like you only casted 16 Shield Charges throughout the Rookery when looking in depth, and only 15 Demo Shouts as an example. In addition, only 13 Demolishes, 9 Ravagers...
Shield Charge and Demo Shouts are notable ones, since those have less than a 1m CD without cooldown reduction. It looks like you don't have tier 4-set, which makes it not as bad, but
You should still at least match casts to the number of minutes you were in the dungeon, counting downtime in there. That leads up to a tremendous amount of rage lost, as both of those generate rage, and Shield Charge also applies Shield Block, which hurts your uptime. You're also ultimately criminally underutilizing defensives as a whole as a result, since you only had 10 casts of Shield Wall the entire dungeon; it has like a 1m CD when playing well, so you absolutely could have gotten more casts out even when not playing particularly well over the course of 23 mins. Heck, with double wall talent picked, it goes down to a base CD of 2 minutes, so you at least should have gotten at least 1 more cast in even if you didn't get a single second of cooldown reduction.
This also extends to your base rotation, as well; your highest CPM on Shield Slam of the three dungeons here is 8.8 casts per minute. This should, bare minimum be at least above 10 CPM, though you can definitely get closer to 12 CPM and beyond. This is indicative of you sitting on shield slam resets, just letting it sit off CD. You're almost certainly prioritizing Thunder Clap over it sometimes, even, since you have more outbursts sent on Thunder Clap over Shield Slam; preferably you send all ourbursts on Shield Slam, so sending more on Thunder Clap than Shield Slam really hurts.
This all comes back to hurt in a major way; all of these cost you a lot of rage over time, which is rage that could be fueled into both Ignore Pain and Revenge, increasing your survival from more absorb strength and more leech, respectively. This also costs you spending that could be rage, which means you get less cooldown reduction on Shield Wall and Avatar, the former being survival and the latter rage+damage, and it also costs you less outbursts over time, meaning less damage and less rage. That lowered rage again hits you a second time by repeating this process at the start of this paragraph. A lot of Protection Warrior is a feedback loop that feeds into itself; the more you do, the more you gain. The less you do, the more you hurt.
Most of this seems to be from struggling to play the spec at a baseline level due to unfamiliarity and lack of muscle memory. I'm kneejerk thinking this because you're also leaving tons of interrupts on the table. You yourself only stopped 7 casts, while there were tons more potential stops that were missed by the group as a whole. You could have pummeled more of them, or storm bolted, even leveraged a shield charge if it happened to come off cooldown, but it's likely you're spending more time fight the spec than you are the content.
My recommendation would be to practice at the training dummy for like 5-10 minutes every day (don't do too much more or you start to try and teach fatigued muscles, leading to ingrained mistakes instead of clean play; the repetition is more important than the length of sessions generally), focusing on sending all of your CDs on CD properly. Make sure to press Avatar when it's back up, Demo Should, Shield Charge, Ravager, etc. Remember to always send Shield Slam once it's back up, as well. You can focus on Outburst management later, when you're more accustomed to actually sending your abilities on CD properly. Also remember to properly spend your rage; if you get close to capping rage, send it on Ignore Pain. It doesn't matter how much IP you have, if you've recently pressed it, whatever. Just treat it as a rage dump, and you'll get the value you need out of it when playing properly.
split lake
restive moon
ripe lake
