will purchasing the game on here unlock the full game and future updates or will I need to eventually purchase the game elsewhere in order to complete it?
Itch.io and GOG are one-time purchases. You buy the game, and all future updates.
Patreon/SubscribeStar/Boosty are a monthly support which allow us to develop the game, with the added benefit of being able to download the current version. So if you want to own the game, I’d recommend itch.io or GOG when it releases there :)