Aurora Store - Install Google Play Store apps without a Google account - I recommend to switch all non-paid apps to be installed with this, and use an anonymous login if possible.
F-Droid: Install apps from centralized repositories (like a package manager) - I recommend to gradually switch all FOSS apps to be installed with this (not all Google Play apps can be installed with F-Droid of course). Other repositories can be added.
Obtainium: Install apps from the ‘releases’ page of the app’s Github/Gitlab - I prefer this to F-Droid if possible, but there is little difference and it is slightly harder to set up, so I don’t recommend this initially.
And last of all, installing an APK manually from the internet (works similar to an EXE installer).
Each of these options should work on all Android distributions or ROMs.
For those who dont know these already:
Aurora Store - Install Google Play Store apps without a Google account - I recommend to switch all non-paid apps to be installed with this, and use an anonymous login if possible.
F-Droid: Install apps from centralized repositories (like a package manager) - I recommend to gradually switch all FOSS apps to be installed with this (not all Google Play apps can be installed with F-Droid of course). Other repositories can be added.
Obtainium: Install apps from the ‘releases’ page of the app’s Github/Gitlab - I prefer this to F-Droid if possible, but there is little difference and it is slightly harder to set up, so I don’t recommend this initially.
And last of all, installing an APK manually from the internet (works similar to an EXE installer).
Each of these options should work on all Android distributions or ROMs.
P.S. Please consider using a FOSS android ROM, such as GrapheneOS, LineageOS, /e/, CalyxOS, etc.