plc000 I just want to point out that Google Maps doesn't require Play Services for basic functionality. I only install the Google Services Framework component (without any permissions), and Google Maps works fine for looking up addresses, getting directions, etc.
plc000 If I use Google Play Store (with a dummy account created in the Play Store app, no phone number) and Google Maps, do I gain anything in terms of privacy compared to - say - using the stock Android my phone came with?
Unlike stock Android, you gain the ability to dynamically toggle the various permissions for all apps, but that's about it. You would be interacting with the Google Maps app directly, so any information you provide it will be made available to Google regardless of how you installed the app.
I don't believe that the re-routed location services would mean much in this case either, since you would be providing the location data directly to Google anyway.
plc000 I would also like to avoid having to switch profiles when I just need to quickly look up an address. What is the general recommendation from the community?
If it is a simple address search, consider using the Google Maps website (or any other mapping website) within your browser instead. You can even "install" it as a progressive web app (PWA). Just browse to the site, go to your browser menu, then select "Install app".
plc000 I also read on the forum that there is no privacy gain installing applications via Aurora Store with a dummy account versus just doing the same in the Play Store.
My understanding, from the official Aurora FAQ, is that Aurora acts as a proxy to the Play Store when an anonymous session is used.
For anonymous logins, following data is sent to Aurora Dispenser Server:
a GET request to obtain an authentication token. This token is generated server side so no user data is leaked. Requests upon creating sessions are made and sent to Google from the dispenser server's IP.
So, not only are you using one of the pooled authentication tokens provided by Aurora, the connection to the Play Store itself is relayed.