I personally think splitting the party is fine but with caveats.
As a player, I don't mind to just sit back and watch for a while, take time to think about what's going on, quietly chat with other players and discuss the events of the game (having a separate room is a godsend), and also go for a smoke, text my boyfriend a little, and otherwise take a break from the game. Obviously I don't want to do that the whole session, but 30 minutes? Sure.
I would be significantly more annoyed if the GM was like "okay, meanwhile, and what are you doing?" every five minutes, thus requiring my actual attention, while not being able to do anything. That's exhausting! I don't want this spotlight, keep it.
That's why as a GM I do it exactly like that -- give one group a significant chunk of the time, then the other, instead of them being simultaneous. I also aggressively skip time to keep all the groups more-or-less in sync.
I also don't worry much about players learning things their characters don't know. It's okay, and, frankly, it's better if they act on it! Like, that's the benefit of someone going for a scouting mission -- to give intel. If players then are forbidden from using that intel until scout returns and tells them that in character, what's the point? It's annoying.