I'm not familiar with card based games but I could give my insight about your game idea.
I'll start with this: You've posted 3 game sections in your game. I got impression that each section have their own cards, IOW player would need to manage 3 set of cards: for boat, island and battle/fight. Am I wrong? or the cards are only battle cards?
then this:
Boat management (space management)
Therefore, you choose which card to keep and balance with fewer good cards (which take more space) and many bad cards.
I had assumption that this section would have its own cards, So, what does each card do? aside of filling space in limited boat space that is.
Do they cards define number of supplies for the travel? if the answer is yes, it will affect the other 2 sections: map navigation and battle.
At the end of the island, the player gets 3 new cards.
I was going to ask something but it's similar to my first question above so let's go to this next question: since boat space is limited, will player be required to rearrange cards again in their boat?
Oh yes, I suggest setting different number of reward card based on difficulty say Easy gives 2 new cards, Normal 3 and Hard gives 5 or 1 very powerful card.
the player can run away from the island, but they will lose something (card, money, health, ...).
This sounds complex. I understand about card and health but with money you'd need to create a system where money is needed such as shop.
Fight
To play cards, you select which card you want to play and the order. The game will simply play the cards in this order.
I am imagining Slay the Spire and regular turn based RPG battles. My question is basic but you have to answer it to construct the base of your game: how would the fight be? 1 vs 1 or 1 vs ? ? The latter means number of opponent varies, sometime you fight one enemy but in other times you fight 3 to 5 enemies at once.
If the answer is the latter, in a fight with multiple enemies, will attack cards target all opponents or target a random single enemy?
I think my post is long already but it should cover the basic questions.