Hey, I actually wanted to come back here because even though I had to restart I did "beat" the game. I saw all the content there was to see it was fun, I don't know if you need a save system, obviously it's going to feel like it at the moment because it's unfinished. I will say though that not having one certainly made the above task a lot more strenuous with no real upside. What I wound up doing was simply farming it out and recording every single animation that way if I do want to use this game for part of it's intended purpose, I can just do that. This made me realize that if you do want this game to be a rougelike it probably doesn't need a save system it just needs a gallery and then you should take some inspiration from Dead Cells (people are always going to want a save system even if there is a gallery because they have to RE-grind everything to get to content further along, Dead Cells gives you checkpoints of sorts and lots of along-the-way upgrades that mean you don't have to repeat the same grind there's just a new grind for the content you didn't get all in one run, rather than just redoing all of that stuff). I don't actually know if Dead Cells is the best example there, just trying to give some constructive criticism or an alternative to saving. I think a way that could happen in your game is to simply have the characters be unlocks that are in different spawn locations/bases, that way certain things are locally accessible on that characters play through if that makes sense. Good luck, I liked it, I think it'll go pretty far and has a lot of potential regardless.
Side note, what is all the supply stuff people are talking about? I never used that, might've missed some content.