Disclaimer: I’ve only leveled to 28 so far and am still stuck in Heresy. I haven’t tested everything, but this is what I have to say about it all so far.
Edit: I’m 30 (+22 additional levels now).
Arbites Shock Maul: Feels good. Enjoyable. I’m not sure how effective the special attack stun really is. I can’t see a big difference in clubbing their brains in, vs. adding a special stun attack into the rotation. In Psykhanium, the damage output is lower with it in rotation, the trade-off being a stun. Generally, just killing stuff seems more optimal. Although I think the old Shock Maul special attack is cooler, I think it’s more inefficient as you are locked-in to the animation, leaving you vulnerable (a bit of a gripe I have with chain weapons as well).
Edit: I’ve fully removed the special attack from my rotation, and I think the Arbites Shock Maul is the best melee weapon Arbites has. Superior to the old Shock Maul and its two variants.
Executioner Shotgun: I like it, and the way it sounds. It does well on range too. I try to use the special ammo, but there doesn’t seem to be a good time to do it. So a lot of the time, it goes unused. Maybe that will change when there are more challenging situations in Auric.
Edit: The Mk 8 has become my main gun of use for my ranged spec. There I do use the special armor piercing shell all the time. Especially in higher difficulties and Havoc.
Dog: I think it’s a fun addition, but it can be confusing when 4 of them are jumping around left and right. That issue will die down as people go back to playing their old classes. An issue I’ve seen with the dog is the AI and pathing. I assume that this is because it uses the same AI as Pox Hounds. At times, there is a delay before it takes/executes an action.
I had an instance where a Pox Hound was coming for me, as I marked it to be pounced, the Pox Hound stopped, looked at me, I stood still, looking at it, my dog stood still, looking at it. It felt like a good 1.5 seconds, well enough time for me to swap to shotgun and blast it to the Warp. Then it happened. The Pox Hound pounced me, then my dog pounced it to remove it from me. I’m not sure if you can speed up the reaction without breaking balance or affecting the Pox Hounds. But it is something I’ve noticed more than once.
I think the positives of the dogs outweigh the negatives. So you don’t interpret it as I think “the dog is shite and bad”.
Arbites Talent Tree: A big upgrade to older talent trees. Which I’m sure you already know. It’s well organized, it’s easy to get to the good bits, and it has a lot of interesting talents to pick. I’ve mainly played Remote Detonation, Arbites Grenades and Break the Line. All three have been enjoyable to play.
I like that Remote Detonation has self-regeneration of its charges. And I go Lone Wolf to have the same perk when playing the Arbites Grenades/Voltaic Shock Mines.
I have limited time spent with Voltaic Shock Mine. It’s not terrible so far, but the range does seem small. It works in cramped spaces, but anywhere larger than a hallway, it loses a lot of its effectiveness. Also, I think the enemy density on lower levels is part of the perceived ineffectiveness.
Edit: It’s an excellent addition to Havoc. Higher density and tougher enemies really makes it stick out. I don’t like the amount of time it takes to swap to it and deploy. I can understand this as a balance thing.
Execution Order: It’s like a good Disrupt Destiny version. The enemies are easier to see because the coloring is better. You only need 1 kill to Rock and Roll (fully buffed). And you can have multiple enemies marked at once. Although it’s limited to Specials and Elites (Monsters and Captains too). However, in higher difficulty, even in Heresy, there’s always someone waiting to be converted into a buff for me.
Deluxe Edition Cosmetics: I like the frame. The weapon skins are a bit meh. I guess they’re okay if you want to go with a more black theme on your character. The armor is nice, and the dog skin is nice. I’m not a huge fan of the Mr. Sparkles mouth effect. Makes me think it’s defective. 
Mission Map: I think this was a step back to what it was previously. I know it’s nitpicking, but I liked the mission images better before, and I don’t think the animated background as you click a mission was necessary.
[Bug] I’ve also noted that, when I open the map, I can’t click “Play”, even though Quickplay is automatically selected as you open the map. I have to select a mission and then Quickplay again if I want to Quickplay.
The Mauler Voice: I think it’s hilarious and cool. Me and some other players I was playing with, were imitating the voice lines in the in-game VOIP and laughing. Probably the best addition with the update/DLC. Like everything else voice and sound related in Darktide, it’s very much top-notch.
Updated Weapons:
Shotguns: I used them a bit before the Arbites was made available. They’ve become more consistent with getting a 1-2 shot kills against Specials and various Elites.
Tactical Axe: It was always solid, but now it feels even better, especially on my Zealot. The damage is up and scoring weak spots on Plague Ogryn has become a lot easier.
Shock Maul, Eviscerator and Catachan: I’ve only tested them out a bit in Psykhanium, so no educated verdict other than, they feel a lot better.
Inferno Event: I like the esthetics of the event. However, it does seem very uneventful. There are a lot of Flamers around, but they walk slowly, and don’t seem to make any sounds when walking or shooting. I thought the event would be like Hunting Grounds or Waves of Mutants, where you would be assaulted by 5-10 Flamers/Bombers mid-horde. It’s not the best event I’ve played in Darktide.
Edit: Getting to higher level has improved the event experience. Especially in Havoc when it has Inferno modifier.
Difficulty Unlock: I was under the impression that seasoned players wouldn’t have to spend a lot of time unlocking difficulties. I probably misunderstood the post and that, old characters are the ones who you won’t have to unlock it with.
That said, I’m level 28 with Arbites, I still have 2 more missions in Heresy to get to Damnation, and I have over 2.6k hours in the game with about 3497 levels on my account. Let me tell you, Heresy is too easy, and it is not super fun. It’s not the end of the world, but I would have liked to see it done differently. Maybe when you release the next class (THIS YEAR??? 
), I won’t have to suffer as I have suffered today.
Okay, a bit of an exaggeration. But I do think it is not as fun as if I would have played Damnation/Auric only.
Stability/Connectivity: I rarely ever have issues with connection. But, and it’s understandable today, I’ve had a couple of disconnects today and some higher latency games (around 60-80ms, OH NO!). Nothing worth mentioning really, but at the same time, I think it should be mentioned. 
Considering the player numbers have 5-6x today, I think it has worked really well. When I got hit with a 3k+ queue, I was a bit worried, but that took about a minute or less to clear.
Mortis Trials: There has been a big improvement on this mode. Elites and specials on every wave as far as I know. Wave 3, 6 and 9 are occupied by waves of Monstrosities. It’s a lot more hectic and fun. Still quite easy due to the insane buffs you get, but still better than what was. 
Summary: Overall, very positive. 