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dext Do I understand correctly, that locking the private space is an equivalent of stopping a user profile? This means that after locking, apps in private space won't run and receive notifications?
That's correct.
dext So if I'd use Play Services on both, the only benefit would be a separate VPN, right? It doesn't make sense to use it to add extra protection for some critical apps, like e-mail, banking, gov id, etc.?
You can use it for its two use cases, 2 separate VPNs and sensitive applications in Private Space, it's also useful for users who don't want to install Google play services in the main profile, even though it runs completely sandboxed with no privileged access in GrapheneOS.
Private space is a more powerful and efficiant workspace, it doesn't require a third-party application and isolation is much more robust.