I think I get what you're going for here, but honestly... the skills themselves seem to have been left lackluster to accommodate the dual-gauge, instead of the effects (rather than merely the resources) of the dual-gauge being really milked/made milkable to grant those skills depth. It's a good enough direction but something just feels slightly... bland, about it?
(Of course, a lot of that will come down to my comparing it with pipedream revisions of combos so that we needn't (technically or just effectively) hit 111222111333222111 etc.)

Not sure why people are hung up on the stun, as more mobs can be silenced and pacified than stunned, so this would actually make it more reliable -- though at cost of diminished AA damage taken, easier positioning for melee, and a secondary CD. But, honestly, I too would prefer to just see it as a stun, and then have stuns automatically degrade to silence/pacify when the target is stun-immune. I'd also prefer it again be called Brutal Swing, albeit in the same RA slot as Low Blow and, say, Riot Shield.

I don't much mind the Provoke change but at the same time, it, too, seems... a little off? I'd like to know more of the context of MP usage across all tanks, though, if I'm to judge it fairly.

I don't like Onslaught being pushed to a 30s CD. I prefer it be a damage-loss-unless-saving-a-GCD-of-uptime with good alternate enmity generation utility.

Furore reminds of when we literally had a skill called Barbaric Yalp, but more importantly makes me question the MP usage...

Equilibrium now seems a bit... weird? I would have figured it'd have more to do with equilibrium now that you have a dual-gauge -- e.g. by granting half the lead of one gauge to the other and then boosting both by half of the lower gauge's value or whatnot -- Or at least giving gauge-scalar HP and MP, even if that might make it a little less obvious or easily accessible/reliable. We seem to have that in spades, and I'd honestly prefer a few more moments of glory on Warrior over simple unvaried reliability. That's just personal preference, though, ofc.

Inner Calm doesn't seem very Warrior-like. There's doubtless something nearly synonymous that would, along the lines of a battle trance, but this isn't quite that. I'm also not sure a consumable ability is the best place for a self-HoT, even if I do like the synergy/anti-synergy of it? It feels like a lot has been left disconnected to the gauge systems that could be deepening them without making Warrior overly sluggish to accommodate changing situations.