It’s normal behavior since you’re starting VNC server for user user.
What do you need it for?
I guess you can do this by configuring the VNC server accordingly, maybe something like this:
https://wiki.archlinux.org/title/TigerVNC#Running_Xvnc_with_XDMCP_for_on_demand_sessions
But this is general Linux question and not really specific to Qubes OS.
Because the VNC is running for the user user specifically and not as system service so there is no point trying to switch to another user.
You can try to run the script using .desktop file: