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coffeefun Most of the apps I already use are available as APK downloads (e.g., Signal, Protonmail, Standard Notes), and I would prefer to switch to other FOSS apps for things like weather and maps. So, for most of my usage, I don't actually need Play Store (I can forgo notifications). If I really wanted to avoid Google, it sounds like using RSS for APKs offers more privacy than Play Store while having an equal level of security. Is that correct?
Not necessarily. Getting your apps through APK downloads, no matter which way you use to track updates for them puts the onus on you to ensure that the APKs you're downloading are legitimate, and that you're updating on time.
For example, you will need to ensure that the first download is legitimate by verifying its signature with a tool like apksigner. Furthermore, to use the example of Termux that someone mentioned above, their GitHub Release (which is likely what you'd use when going for the "RSS method") is signed with a test key that many people in their community have access to. That makes it trivial for someone to create and sign a release with the same key that you think is legitimate and trick you into downloading malware.
On Android, when you download an app, you can only update it if the signature of the initial install matches. If the signature is leaked (intentionally or not) and used by others, or if the initial download is not the legitimate one, this protection isn't worth much.
These are the kinds of things you won't have to worry about with Play Store since you obtain Play Store itself from "Apps" which provides a very high guarantee that you're getting the legitimate app, and then of course apps you download from the Play Store also have guarantees that they're legit, unless you unintentionally download a copycat (they exist).
coffeefun would I be able to create a "Music" profile to install Google Play and Spotify, and continue to stream music from the Music profile while using my owner profile? And, perhaps more importantly, does this strategy provide real benefit from a privacy perspective? And, does running two profiles impact battery life?
You can't realistically do that with user profiles. When you switch to another user profile, your music will stop playing. The benefit there is also dubious. Spotify wouldn't be able to see or communicate with the apps on your owner profile, but are you assuming that it tries to do so anyway?
And, does running two profiles impact battery life?
In some capacity, I'm sure.