I have zero idea about technical underpinnings, so maybe I should just remain
silent, but...
Linux Lite is also Ubuntu based, so it may be easier to use some of its code
than non Ubuntu based distros.
https://www.linuxliteos.com/manual/software.html#instsoftware
It seems to have two interesting "helpers".
Lite Software offers a seemingly curated, de-mystified list of "popular" apps
and other installs.
https://www.linuxliteos.com/manual/software.html#installsoftware
Similarly, Lite Tweaks is a list of available system tweaks.
https://www.linuxliteos.com/manual/software.html#tweaks
Obviously, neither app is inherently protective of users' freedom, but that
could simply be a matter of what a given distro's developers and repos
choose. Both apps are also very basic, with no screenshots or reviews, and
likely a very limited selection given the apparent assumption of a list that
can fit in a single window. Still, FWIW.
And what about ElementaryOS? It's also Ubuntu based, and while the Pantheon
desktop environment is tightly integrated across the OS, it's at least based
on GNOME just as MATE is. And its App Center (selection visible at
https://appcenter.elementary.io/) combines Apple like slickness with a "pay
what you want" style that doesn't necessarily undermine an ethic of sharing
but does easily enable direct user support for developers and projects. Once
and if ported, this may reduce the workload and debates associated with a
tightly restricted and curated list of apps such as in Lite Software.