It is really the case that you own your notes, even if you use the Obsidian mobile app downloaded from Google Play. Google Play just distributes the app. You do have to agree to grant the app permission so that it can function, but these permissions are limited to what the app needs to function properly. For example, it wouldn’t work if you didn’t give the app permission to use the storage on your phone. When you grant this permission, you are giving permission to the Obsidian app, not Google.
The only way Google would be storing your Obsidian vault would be if you chose to store it in Google Drive. Even then, however, you still legally own your data (at least according to Google’s current TOS).
I would recommend you also make sure that your phone is encrypted. I know with Google Pixel phones and iPhones, this is done by default. I don’t know about Samsung and other manufacturers.