Outline client app as VM

[apparatus]

Create a separate sys-vpn qube, connect the qubes like this:
sys-net ↔ sys-firewall ↔ sys-vpn ↔ sys-whonix

The Outline VPN should work the same way as other VPN apps, you can follow this guide as an example:

Mullvad VPN setup guide

Using Mullvad VPN on Qubes OS | PrivSec - A practical approach to Privacy and Security This is my setup for Mullvad VPN on Qubes 4.2. It differs from solene’s guide in that it uses systemd path to trigger /usr/lib/qubes/qubes-setup-dnat-to-ns. No rc.local (which is legacy stuff and shouldn’t be used anymore) required. You can also create multiple Mullvad ProxyVMs from a single template instead of needing to use standalone VMs.

But instead of installing mullvad app in the template, move the outline appimage to the sys-vpn qube and run it there.
Also you may need to apply the MTU fix:
Wireguard VPN setup