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1 day ago I was just reminded about Amazon Fire Tablets, which are somewhat common and don't run GMS. They can sideload apps and app stores though so F-Droid would be potentially good for this purpose. Might also be worth looking into releasing on the Fire Store.
Currently Android native releases are available from the Google Play Store or direct download from GitHub. Given that the direct downloads don't auto-update (and can't, at least easily), most people are probably better off using a version distributed from a store which support auto-updating (or using the web app.. but currently it's not quite as functional unfortunately, from some issues out of my control).
So that means currently the Play Store is the only way to do this. A lot of people use it because it's preinstalled and uninstallable on most Android devices (GMS), but it would be good to have it available on a different one I think. The app doesn't use anything that relies on GMS at all so there shouldn't be any issue with this. F-Droid seems like a good alternative because it's relatively popular (at least as far as 3rd party mobile app stores go at the moment), to my understanding hosts exclusively free and open-source (FOSS) apps, which Galaxy Collection is, and generally has a much better philosophy and ethical approach than most app stores. This would enable people who don't want to or can't use GMS/Play Store to still have an auto-updating native Android release of Galaxy Collection, and hopefully also help with discoverability and reach a bit.