Is it possible to use the built-in VPN client in the work profile?

As the title says, I'm looking for a way to set up the built-in VPN client to work with the work profile (under Shelter/Island). There's no separate Settings app in the work profile to allow that, or an option to specify the profile when adding a VPN configuration in the main settings app. Most online references to VPNs in the work profile mention third-party clients; however I need to connect to an L2TP/IPsec VPN, and AFAICT no such client exists. Google's VPN documentation says you may need a separate VPN app "to run a separate VPN for the personal profile or work profile" - but I don't want that, I just want to run the one VPN, under the work profile. On a separate page describing the built-in client it says "you can make a VPN work only for apps associated with your work profile", but does not explain how, and I'm not finding such an option. Any help appreciated!