Web Apps & PWAs :) There's a lot you can do to optimize offline PWA use.

PWA Babyb~~~~

Ask Epic how that worked out with Fortnite...

As mentioned this is possible but not recommended for Android. I'm not sure if anyone is releasing paid apps outside of Play store though.

On iPhones, Apple forbids third party appstores. You cannot also sideload. So that's a no go.

On Androids, I think you can install third party appstores. fdroid is the one I've heard before, but there could be more.

Most of these [0] started as desktop software but some have extended to mobile devices in ways that can interact via cloud with the version on your desktop, if I'm not mistaken.

[0] https://www.artisanalsoftwarefestival.com/