Docker on Linux allows Xdebug to automatically connect back to the host system so you can just set xdebug.remote_connect_back=1 and leave out the xdebug.remote_host in your xdebug.ini.

Works for me on Ubuntu 20.04.

Add to you project's docker-compose.yml

(https://github.com/docker/for-linux/issues/264#issuecomment-772844305)

services:
  your_php_service_name:
    extra_hosts:
      - host.docker.internal:host-gateway

In your CLI run export XDEBUG_TRIGGER=1 && export PHP_IDE_CONFIG="serverName=host.docker.internal" to start xdebug with the request.

Thanks @LazyOne for his comment to the question with the solution.

After booting up my machine to investigate further with the comments of @abestrad and @LazyOne, without changing anything, opening localhost:8080 suddenly let the debugging work by stopping at the breakpoint that I have set. Actually I had already tried to restart the Docker Desktop App before writing the question, maybe at that point my configurations were at a wrong state.

But at the end the solution was: Restarting the PC.

Watch out

To be sure i tried to open it also in a private browser session and it wasn't working anymore. That was because the special cookie still was set in the normal browser store (cookie that was stored either from the Browser extension that I have already uninstalled, or from trying out the JetBrains Bookmarklets generator before writing the question).

The solution to let it work everytime was to add following:

xdebug.remote_autostart=1

Citate from here:

Normally you need to use a specific HTTP GET/POST variable to start remote debugging (see Step Debugging). When this setting is set to 1, Xdebug will always attempt to start a remote debugging session and try to connect to a client, even if the GET/POST/COOKIE variable was not present.