I suspect this issue may be due to DNS requests being routed into the VPN app which is active in the owner profile.
I have not tested this. (tested by d4f2 report in reply below)
My understanding is that DNS requests from any user profile all use the same route as specified by the network.
You can override this by using private DNS which changes DNS everywhere. Including routing all DNS traffic from any user profile even if they have VPNs active.
If private DNS is not set then a VPN app in a user profile will have control of routing DNS requests from that user profile - often the VPN app will be set up to route DNS requests from that user profile through itself.
I suspect that a VPN app in the owner user can end up routing DNS requests of all user profiles which dont have a VPN app active which is routing DNS requests through itself.
You could try disabling the VPN app in the owner user and instead installing and activating one in a secondary user to see if the banking apps, which are in a secondary user without an active VPN, then stop complaining about a VPN.
Can also explore this with web based DNS checking services. Could run such checks from a web browser in a secondary user, which does not have an active VPN app, while you have your VPN app active in the main user. See where the service reports the DNS checks are coming from.