Add an additional flag guard for Private Space implementation

This a layer of flag guarding only for the implementation of Private Space features excluding the APIs. The MVP flag allow_private_profile still guards all the features including the APIs.

Bug: 326060689
Test: Manual - a few verifications that some feeatures are unavailable when this flag is disabled
Test: Run presubmits and verify that nothing breaks
Change-Id: I05f7e2f20c6132b33484bb133ce03a933ece485f