I strongly recommend a complete overhaul of the loyalty mechanic. It is counterintuitive and needlessly frustrating.
People leave because your leadership is bad? What even is "leadership"? What's the problem? Not enough food? Lost a skirmish against enemy raiders? What's wrong? Nothing even happens in the first many many weeks anyway, there's no reason for people to think you're a shit leader. In fact, you are in control of a stronghold containing a substantial food reserve in a world lacking in security and resources. Why would some random girl who joined you because of starvation want to leave because you have "bad leadership"? If people leave in the very next turn because you're such a shit leader, how come they even joined you in the first place?
Your first company is eternally loyal to you no matter what you do? Why? Keeping the loyalty of your soldiers would be an interesting gameplay mechanic and really, it's the loyalty of your soldiers that should matter most in this kind of game. Your soldiers being immune to desertion gives an incentive to make the leadership mechanic ridiculously severe for anyone else that joins you, as a counterbalance. Loyalty should matter to everyone to make a sensible gameplay mechanic.
The first "mission" is a terrible implementation. All you can do is click "explore". You don't make a single choice that matters. And the only correct level up for yourself once you get enough xp is stamina, anything else is a wrong choice so it's not really a choice. The grind is unreal. There should be something to actually DO in the beginning of the game, any choice that matters.
I really like the concept but the gameplay and UI need a lot of work to even be passable.