Domain-level forward-auth with a dedicated outpost returns 400

## What

domain-level forward-auth + dedicated outpost: 400/wrong session, and the admin snippet is wrong for a dedicated proxy outpost.

## Want

- Domain-level forward-auth + dedicated outpost: 400/wrong session,
- The admin snippet is wrong for a dedicated proxy outpost

## Ideas this came from

- [#10848 Error 400 on Forward Auth (domain level) via Outpost](https://github.com/goauthentik/authentik/issues/10848) — I created Forward Auth (domain level) and provider (using wizard), but it works only with Embedded Outpost correctly. With Proxies, it returns 400 (in logs wron
- [#20317 Forward auth domain level example in admin console is inaccurate when using dedicated proxy outpost.](https://github.com/goauthentik/authentik/issues/20317) — Do you see an area that can be clarified or expanded, a technical inaccuracy, or a broken link? Hi, I believe that we should clarify that if we use a dedicated

Start by reproducing domain-level forward-auth with a dedicated proxy outpost and compare it with the embedded outpost behavior. Inspect the admin-console snippet for this setup. Done means the dedicated-outpost request no longer returns 400 or the wrong session, and the snippet accurately describes the configuration.

Written by the indexing model from the issue text.