I think how the genetic augmentation ban was portrayed in Una's case in particular - a military court martial - was similar to "Don't Ask Don't Tell", so LGBTQ+ groups do seem to fit better than, say, race or sex. Even with DADT no longer in force, there's topical parallels, like you suggest, with trans people. But there was an emphasis on the Illyrians' genetic augmentation being "their custom", so you can apply religious or cultural prejudice equally as the allegory.

One of the problems that this show has to grapple with is that we already know Spock very well from Leonard Nimoy's portrayal. I'd go so far as to say that - notwithstanding a few gaps - every major event of his life is known to the audience, and we are very familiar with how he's "meant to be".

What then is an actor to bring to such a part? Ethan Peck can't just replicate Nimoy's performance - for one thing, it would be boring. The writers take advantage of this series being a prequel to do the only thing they can: show how Spock became the Spock that we know from TOS. They use his appearance in the TOS pilot "The Cage", where he was visibly more emotional and "human", as a touchstone, and make his journey towards emotional control and "Vulcan-ness" part of his character arc for this show.

I went into it a little in another post, but I think Spock's manner is more familiar and "one of the guys" because he's allowed himself to become emotionally attached to the rest of the crew, and that bleeds into his personality, making him more liable to use humour and jokes to relieve tension. A few years later, when Kirk takes command and many of these officers have moved on, he decides that he will be more emotionally guarded, letting his guard down only with Uhura and Chapel - and only in brief, relaxed moments.

Sort of - the mystery of what happened to Chakotay is unresolved, but the crew got a more-or-less happy ending. From how it's being reported, season 2 is all but complete and they just need to find a new network or service to show it - I'd wager Prime Video might be a possible home for it as they've historically had distibution rights for the various other modern Trek shows internationally.

Completely agreed about Spock's emotional journey. It's also important to note that Spock's relationship with the crew of the Enterprise is far more familial and personal at this time than it is TOS. Look at how Ortegas and Uhura tease him mercilessly on the bridge, and he indulges them with an air of bemusement. I think that by the time he becomes Jim Kirk's first officer, years from now, he will have seen this close-knit group of officers move on one by one... and as friends come and go, he'll adopt a more distanced, some might say more professional attitude, one that he considers befitting of an executive officer.