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Privacy1st Does private space have a separate Advertising ID, Android ID, IMEI, Mac, etc? Do separate graphene profiles have these?
Apps cannot access your IMEI or MAC or other persistent hardware identifiers. Except for the Vipewine DRM identifier, but that is rarely exploited and will be fixed one day by putting it behind an app permission. At least so I heard.
Advertising ID is a Google Play feature, so doesn't exist on GrapheneOS at all by default, only if you install Google Play Services. It should be different for each profile, since no app can communicate cross-profile on GrapheneOS, not even Google Play Services. You should even be able to generate a new random one in Google Play Services settings, to change it for that profile at any time.
Your phone number will be accessible to all apps that you have granted phone or SMS permissions to. That can be seen as a persistent hardware identifier I guess, so avoid granting that permission to apps that mustn't know.
Privacy1st If I have an app using Bluetooth/wifi in my private space, will it appear as a different device from my owner profile Bluetooth/wifi connection?
I cannot answer for Bluetooth since I never used that. But each profile can have its own VPN connection, and thus its own outwards facing IP address. And other than the mentioned Vipewine DRM thingie, there should be no way for the app to get a persistent hardware identifier or cross-profile identifier.
But even if your device cannot be exactly identified as the same between profiles, there are fingerprinting possibilities that might statistically reveal the profiles are running on the same device. For example what device type (eg Pixel 7a) you are using, at what times during the day you seem to use your phone, that the two profiles are used similarly close in time or even interleaved in time but never used at exactly the same time, your country you are in since that cannot be faked yet, when the app got an update since apps are updated in all profiles at the same time (this is especially revealing for Google Play apps because of staged rollouts), and much much more. Depending on your adversary you might need to be mindful of that.