I can only answer the questions that relate to usability, based on the user-facing interface of the Private Space feature in Android 15 Beta on stock PixelOS.
ryrona If I have understood it correctly, the private space can have an always-on VPN set up even if the main user does not have any VPN, and all apps in the private space will run through this VPN.
You can install any VPN app in the Private Space (PrS) profile, and choose to only use it in the PrS. You don't need to have or use a VPN in Owner. The Owner and PrS have separate VPN slots, and "Always-on VPN" and "Block connections without VPN" can be configured separately in the Settings app (opened from Owner). Screenshot: https://ibb.co/F3cD1zj
Notice that the Settings app distinguishes between the PrS and Owner VPN slots by adding a tiny icon to the PrS-specific settings.
ryrona All screenshots show unlocking is by fingerprint. Does this mean there is no separate encryption passphrase for the private space?
On PixelOS, you have to unlock the PrS with the PIN/password for the PrS after every device boot. After that, you can use fingerprint unlock for any successive unlock attempts. On PixelOS you can't "end" the PrS session without rebooting – but on PixelOS you can't end any other profile session anyway, without a device reboot.
ryrona Does notifications work in private space?
Yes.
ryrona Are notifications from main user and private space shown together the same, like they originated from the same user?
Notifications from Owner and PrS are shown together in the notification bar and pull-down menu, but the notifications from PrS are tagged with a separate icon. Screenshot: https://ibb.co/BndbBkT
I personally would've preferred the PrS icon to be larger and more prominent, although it matches the size of the notification headline.
The app switcher will also distinguish between actively running apps with the PrS icon. Screenshot: https://ibb.co/n3y1MZ3
ryrona Do they share contacts?
I added a contact to the Google Contacts app in Owner, then opened the Google Contacts app in PrS: the PrS did not show any contacts. So at least UI-wise, they don't appear to be shared.