I'm rewatching S1 currently, and I must say the opening 2 parter is one of the best pilots of all time.
IDLE THOUGHTS
1. I like the new klingons
2. T'Kuvma rules, killing him was a mistake
3. Voq rules and is the biggest fumble of this show
4. Why is L'rell's head so long?
It is a pretty good pilot. I also recently decided to start a rewatch of Disco before the new season hits (in like... two weeks!), I consider myself a fan of the show, and... it's kinda hard to keep watching it! It's weird. It's not like the episode is bad. It's just that the totality of DIS being a serialized show reliant on an interconnected story with tons of plot twists just... kinda inherently saps a lot of the show's rewatchability. An episodic show, you can put on any random episode and it stands on its own without context, and you can have a decent time with it on in the background. With Discovery, you can't really do any of that. It's just kind of a fault of the format, and I think something that people will look back decades from now and see it as a flaw or failure of this era of "prestige TV" that's obsessed with serialization at all costs.
Re: your idle thoughts
1) I don't mind the new Klingons. Most of the changes makes sense and actually line up very well with previously established lore. We certainly *hear* a lot about Klingons in TNG and other shows about them bathing in the blood of their enemies and ripping still-beating hearts from the fallen. But we don't actually ever really *see* it because of the nature of 80s/90s broadcast television. The weird designs are othering and help make them feel like the terrifying aliens they're supposed to be in say, the TOS films, rather than the cute caricatures that they slowly became as Worf's character helped provincialize them. There's a lot of thought put into their designs, especially things like the intricate detailing of the ships. It makes the Klingons look both cultured and ancient, which is very consistent with their characterization. Despite all their ships in TNG and onward instead looking like rust buckets haphazardly bolted together, which looks neat and familiar but doesn't completely jive with how they're discussed as a race/culture. (It really only jives with the Klingons as Soviets metaphor, which mostly falls apart/gets ignored in TNG and beyond.)
2) T'Kuvma dying
feels like a mistake, because he's a pretty good/compelling antagonist, and Star Trek - for all its strengths - manages to lack these. But I get why he's set up the way he is, and I mostly support it. First off, Disco S1 - despite what it turned into w/ mirror universe shenanigans - isn't about taking on a blockbuster movie style Big Bad. I get the clear sense that it's thematically more concerned with how to even reconcile and find common ground with an enemy you have nothing in common with at face value. An enemy that has a singular antagonist at the top of a unified power structure is pretty easy to overcome. Not in the actual logistics of it, but in the sense that you've got to either decapitate the power structure and let things fall apart, or negotiate an entente with that person in power. But the Klingons in DIS are boiled down into their more quintessential form of a bunch of loosely affiliated warring factions. And you can't just assassinate a single leader, or open up peace negotiations with 24 different factions that all have their own agendas and cultures at the same time. It really adds to the feelings of despair and futility when you're fighting a war against an enemy that doesn't relent and isn't vulnerable to any of the traditional tactics you're good at because their power structure and society is just nothing like anything you can relate to or understand.
3) Voq is such a neat idea, and making his tether to his humanity being a poorly established love just doesn't land and just feels like cheap melodrama instead. It's something that would have worked a lot better had we had multiple seasons of Tyler built up as a regular officer with deeper social connections with the rest of the crew so that his tether wasn't so flimsy and unconvincing. But Discovery wasn't planning things out that far and also has very little patience in general as a show.
4) L'Rell and the rest of the nuKlingons having oblong heads actually isn't *that* weird! It's definitely incompatible with TOS era Klingons, but that's a given. But when you consider TOS-film/TNG era Klingons:
Their heads are actually pretty bulbus, and there's so much hair in the back that they could easily be hiding an oblong shaped skull back there and you'd never even know it. Of course, the real reason is probably along the lines of: they didn't want to cut off the actress's hair, and had to hide it all somewhere. Which is the reason why a lot of Star Trek aliens have weirdly shaped heads and such. It's why the Ferengi are the way they are, and that rear-head-visor thing they wear on the backs of their heads is there mostly to cheap out on makeup since they don't have to have to worry about the makeup in the back of the head that way.