Using insanely invasive surgery to convert Ash Tyler into a human when the Augment virus should do
Well, he wasn't just converted into any human but specifically Ash Tyler. using the Augment virus would turn Voq into a less Klingony version of himself but that wouldn't make him look like Ash Tyler. There would still be need of futuristic surgery in order to change Voq's various features like size or head form.
total absence of Augment virus/TOS-style Klingons
Tie-in media has suggested that the augmented Klingons were initially seen as inferior but started "overtaking" the Klingon Empire, so maybe we just aren't at the point where the augmented Klingons rose to prominence. And of course we haven't exactly seen that many Klingons. Most of them were from an obscure cult who probably didn't allow any "non-pure" Klingons, remember the "We remain Klingon" stuff T'Kuvma was always talking about? The rest of the Klingons were from High Houses who too may very well be bigoted against Klingon augments.
Spock having a secret soul sister
He didn't tell Kirk who his parents were until they literally beamed aboard and waited until they were taken into custody by his half-brothel to tell Kirk about him. Not telling Kirk, or anyone else, about Burnham doesn't seem too weird.
Here's a quote from Memory Alpha: "
The reasoning for the difficulties in intraship beaming was not stated. A technology capable of transporting a subject over thousands of kilometers without error should
be able to do so over a few dozen meters easily, though one could speculate that the emitters are focused away from the ship, as shown in the technical manuals." It could well be that Discovery specifically has inward-focused emitters, maybe because it is a test ship and chances of dangerous malfunctions are higher, so being able to transport everybody immediately to sickbay might have been higher prioritized. As to Spock's line that inship beaming "has rarely been done because of the danger involved" could refer to only the Enterprise, meaming that intra-ship beaming was rarely done on the Enterprise not on every Starfleet ship.
I highly doubt it will stick around.
women captains in the 23rd century (although that is a shitty one I'm putting it in for completeness' sake)
I don't think the crazy person who was so jealous of Kirk getting a command while she didn't, that she swapped bodies with Kirk by employing an ancient machine that Greg Cox used a lot better in an excellent time travel novel, is the best source for information on the 23rd century. Plus, as you said it's a really shitty one.