Thank you for playing and for the kind words! When the combat is in Auto mode (which is mainly how I tested it) I would say it's an auto battler. It's not as idle-friendly as some of them, since the player needs to give some input between battles by using the shop (or at least exiting the shop) and of course there's manual controls (such as they are) for those who want more of a hands on experience. :)
My main inspirations were Super Auto Pets (and games similar to that) for the shop. The classic Final Fantasy games from the Super Nintendo era for the setting and battle style. And then a lot of little things here and there that are difficult to directly attribute. Being able to choose the character's targets while the game is paused, for example, is similar to the weapon aiming in FTL, but that's hardly the only game with such a feature.