Are you familiar with the Same Page Tool? It sounds like you had expectations that you tried to convey subtly to the group in-game, but this wasn't overwhelming enough to overturn their existing expectations or the conflicting messages being sent by your campaign kickoff's dominant tropes, so you weren't on the same page.
Getting on the same page is the first step toward your players having their PCs act like real people – you can establish your expectation, and the possibility, that they can ignore the common game-like meta structures that are often taken for granted around a roleplaying game. Things like they are all a party and cooperate and they're aiming for survival of their PCs rather than character embodiment are common assumptions that are often necessary for certain kinds of campaigns, because it is easy and expedient to say that some play possibilities are "off limits" in order for the group to focus their game time on the fruitful voids of the campaign.
What appears to be the problem is that you have tacitly broadened the fruitful void, without notifying the players of this strongly enough to make them set aside their (productive, functional) RPG-playing conventions. On top of that you set up the campaign with a very standard "form party, loot dungeon" structure, which strongly conveys a standard "dungeoncrawl campaign" set of expectations that are the opposite of what you seem to have hoped for.
How to get them play their PCs like real people is then a two-step process: first, clearly grant them the breadth of allowed play possibilities necessary to be able to play them like real people. Second, cultivate a group value of character embodiment.
The second is the hardest part actually, and the how can't be covered here because the barriers to doing that are personal and depend on your players. Given that they haven't even yet become aware of the possibility with the first step, I have no data to even begin giving advice on the second.
So, that makes the first step very important: get on the same page, eliminate the assumptions about how to play a dungeoncrawl-type fantasy RPG, and replace those assumptions with explicit understanding that you're aiming for humanist drama in a fantasy context. Once you've had this conversation, only then can you even find out whether your players are interested in embodiment-focused play and what their individual barriers for that are, if any. Be aware that they may not be interested in this kind of play; be prepared to have a conversation that is about negotiating a common ground, and it may not lead to the sort of play you're looking for. It's possibly you'll all get on the same page, but if you can't, that may mean the group can't continue – but that's better than forging ahead with conflicting expectation and play goals.
Talk to your players about your constraints as a GM
Ultimately this is an issue where the party as a group of human individuals playing the game will need to make concessions in their play approach to the limitations of you as a human individual GMing the game. In a perfect world you'd be able to respond to their decisions instantly, allowing you to juggle GMing the two separate groups simultaneously, but from your description this just isn't a possibility. Sit down and talk with your players in person, outside of a game session and explain that the overall quality of the game will be improved by you being able to focus your efforts on the party as a singular group vs. a bunch of individuals or two groups. Naturally the party will split when the need must arise, but you can specifically prep/plan story points where this is indicated (the engine room is on fire AND there are enemies boarding our ship) as a way to signal to the players that this is a split which you are prepared to handle GMing.
Best Answer
"Please Don't Do That."
Players are not born with the knowledge that meta-gaming is [often considered to be] harmful. Not all of them, anyway. But I've found that the vast majority of players, once asked or coached gently a few times ("How exactly does your character know that?") are perfectly capable of performing the mental fire-walling necessary to avoid meta-gaming. And most of those are willing to do so under reasonable conditions, i.e., if they don't sense that the GM is out to get them.
This doesn't mean no one ever slips; fire-walling is not effortless, and occasionally I as a player (or even as a GM) forget who exactly knows what about what. But asking for and receiving a good faith effort is a lot better than any other solution I know.
Occasionally you will have a player or players who are just recalcitrant about this. At that point, bust out the various solutions here.