Domain Level Forward Auth with Nginx Reverse Proxy and Synology SSO server as OpenID Provider not working?

# Question
I'm using Nginx Proxy Manager as a reverse proxy, Synology SSO server as an OpenID provider and Authentik to catch all access to my subdomains and have it authenticated with the Synology credentials.

If the proxy provider in Authentik is set to _Application Level Fwd. Auth_, everything works fine.

**However, how can I authenticate on domain level and access all my subdomains based on this authentication?**

Example:
- I want to navigate to `app.domain.tld`, be authenticated on domain level (`domain.tld`) by Authentik (`auth.domain.tld`), and be redirected to `app.domain.tld`.
- If I then navigate to `app2.domain.tld`, I want to stay authenticated.

# Relevant Info
My domains (masked) for the servers/applications (all dockerized):
`dsm.domain.tld`: Synology SSO server location
`auth.domain.tld`: Authentik server location
`app.domain.tld`: Application location

The Synology SSO server is set up as a _Federation and Social Login OAuth source_ in Authentik and works fine for application level fwd auth.

These two previous issues describe similar problems which didn't seem to get solved:
- https://github.com/goauthentik/authentik/discussions/2780
- https://github.com/goauthentik/authentik/issues/5364

Also, there is a post on Reddit with a similar problem description:
https://www.reddit.com/r/Authentik/comments/1460g3z/domain_level_forward_auth_problem/

My Nginx is as described by the [Authentik documentation](https://docs.goauthentik.io/docs/add-secure-apps/providers/proxy/server_nginx), the only change I made was in the proxy_pass in order to fit my setup (`proxy_pass http://192.168.1.11:11425/outpost.goauthentik.io;` in the `location /outpost.goauthentik.io` section - the public URL `https://auth.domain.tld` did NOT work, even for application level fwd auth !!!).