2days
Lets say youre using a VPN in the owner profile and install the same VPN through the Private Space Settings in there as well. You could pick lets say "New York City" as the location in the Owner and "Washington" in Private Space.
It doesn't help much, but makes tracking you a little harder.
And no, apps can't access data of other apps, that's what Android's Sandboxing Model prevents. I was just talking about one of the many points where online activity across different services/apps can be easier tracked, if you only use the Owner Profile.
Only you can decide if that's bothering you enough to use more than one profile on your phone.