This looks about right, I have a similar setup for unauthenticated services here, with the difference that I’m using NGINX Proxy Manager instead of Caddy. The things I would try/check are:

• Make sure you’ve enabled the proxy provider in the local outpost config in Authentik.
• Declare a common network between the two containers, so that they can communicate without having to go out through the host’s IP. This way you can reference the VS Code container directly by its service name in Authentik.
• I’m not familiar with Caddy, but I would also try changing the code.test.example.com entry to point directly to Authentik’s IP and port (in other words, both entries would look the same). In the config your posted, it seems like Caddy is redirecting through itself.