Not everyone wants to be tied to one show. It's a business decision, not a matter of not liking a production or not having a good time. It's a business, and seeking opportunities to expand.
She cannot be second officer in absentia. Why not Spock takes that position. As a Vulcan he can do both jobs.
I am predicting that Spock will eventually become the first officer. It may happen after Kirk becomes Captain but it will happen. Book it.
Given that above photo shows La'an wearing the Enterprise insignia as opposed to whatever ship's insignia Kirk's wearing, it would seem that by the time the second season comes around La'an will be back on the Enterprise and thus back to being second officer. There's never been a definitive answer as to whether Spock or Gary Mitchell were XO in WNMHGB and indeed, the tie-ins are always contradictory on the matter, and that includes novels that were part of the now defunct "Litverse."
This is a fan misconception. Spock wears command gold/green and has the command 'star' delta (or Flying A as Roddenberry called it). He advises Kirk on the situation, and challenges Kirk's decisions. Mitchell, on the other hand, wears the operations salmon with a 'science' delta, like Scotty and Kelso. In the script, he is only referred to as senior helmsman. All evidence in the episode points to Spock being the XO. Nimoy is the co-star... why hire a guest actor to play a doomed character as XO? Especially since Spock also filled the hole left by the removal of Number One. Also, there's a memo I've read where Roddenberry states the science officer is next senior after the captain. But I defer to @Maurice or @Harvey on that one.
This thread from several years ago has all the receipts in it: https://www.trekbbs.com/threads/spock-was-first-officer-in-the-second-pilot.275608/
In the Discoized timeline, does it make sense for Spock to be promoted to First Officer without being second officer?