I find that the far more likely scenario than they digitally inserted the Captain into the scene. Indeed, it wouldn't surprise me if all Paul Wesley's scenes in this episode were filmed off to the side of the other episodes he was in this season. IE, the Farragut bridge scenes were done while Sehlat's Tail was filmed, the scenes where he's in the Enterprise's lounge while something like 4 1/2 Vulcans or something like that.
I suspect it would probably be easier on the production to have Wesley in to shoot with both episodes separately. At least, that was was the case on all the shows I worked on. Generally speaking, you're always going to just make the actors come in whenever it works best for all the other production needs, and it's just easier to shoot the episode all as one piece if you can (unless you're fully block shooting, which this show doesn't do). You aren't prioritizing actor ease in scheduling unless you really MUST, and I don't think Wesley has enough other stuff going on for that to be an issue.
I think the Captain guest actress was there. She was credited. Streaming Trek usually doesn't credit when it's a re-edit of existing footage.
Which I always found kind of scummy, TBH. It's been a long time since I've read the language in the SAG contract on this, but IIRC it's kind of a gray area where you can probably get away with paying them as if it's a clip re-use, but if you're editing them into a scene as if they are actually in the episode and it's not just a flashback, you really are supposed to be paying them as if they came in and shot that episode separately.
Though I could definitely just be out of date. Perhaps in the current contract, this practice I find scummy is explicitly allowed.
Spock doing a mind meld in public. I guess it shouldn't have jumped out at me since mind melds aren't nearly as private in these prequel shows as they were when the concept was introduced, but it still felt weird to be doing this in the Enterprise Bar and Grill.
This also jumped out at me as a production problem! I would bet that they initially intended to cut to Spock's quarters, then you're overbudget and need to find things to cut, and you tell yourself, OK, we can just absorb that into the bar scene and then we've saved on the additional setups.
I've sat in many a production meeting and watched the producers talk themselves into "it'll work, we don't need it!" We needed it at least 70% of the time! As I think these producers did this time.