Thanks for playing and for the video feedback :)
In fact, to leave the submarine, you have to click on the pictogram representing the exit while standing on an adjacent square. You can't interact with it if you're on the same square.
This can be confusing, so I've prepared an update that allows you to exit by moving to the exit square.
I agree with the idea of buying equipment between runs. It's a thought we had at the start of the jam, but we quickly put it aside to avoid work overload. It would definitely be a great thing to develop on a longer game.