Network issues registering gitlab-runner container on gitlab container in same docker network

I’m trying to register a gitlab-runner docker instance to my gitlab docker instance. Both run on the same host in the same docker network (called gitlab-net):

docker run --rm \
>   -v /srv/gitlab-runner/config:/etc/gitlab-runner \
>   --network gitlab-net \
>   gitlab/gitlab-runner register \
>   --non-interactive \
>   --executor "docker" \
>   --docker-image alpine:latest \
>   --url "http://gitlab/" \
>   --registration-token "thisIsMyToken" \
>   --description "docker-runner" \
>   --tag-list "docker,aws" \
>   --run-untagged="true" \
>   --locked="false" \
>   --access-level="not_protected" \
>   --docker-network-mode gitlab_gitlab-net
Runtime platform                                    arch=amd64 os=linux pid=7 revision=e95f89a0 version=13.4.1
Running in system-mode.                            
ERROR: Registering runner... failed                 runner=thisIsMy status=couldn't execute POST against http://gitlab/api/v4/runners: Post https://my.domain:443/api/v4/runners: dial tcp i/o timeout
PANIC: Failed to register this runner. Perhaps you are having network problems

This is the docker run script for the gitlab instance:

docker run --detach \
  --hostname my.domain \
  --network gitlab-net \
  --publish 443:443 \
  --publish 80:80 \
  --name gitlab \
  --restart always \
  --volume $GITLAB_HOME/config:/etc/gitlab \
  --volume $GITLAB_HOME/logs:/var/log/gitlab \
  --volume $GITLAB_HOME/data:/var/opt/gitlab \

As you can see, both containers run on the same network. When I SSH into a new container on the gitlab-net network, I can curl the gitlab instance by it’s hostname (which is the same as the container name, gitlab) without any problems:

curl -v http://gitlab
*   Trying
* Connected to gitlab ( port 80 (#0)
> GET / HTTP/1.1
> Host: gitlab
> User-Agent: curl/7.68.0

So the networking between the two containers is working fine. In fact, the gitlab-runner container must have gathered some information from the gitlab container via network because it is trying to call it by it’s public domain/IP (… Post https://my.domain:443/api/v4/runners: dial tcp …) which I didn’t give as an argument in the run command (only the local hostname of the gitlab container is mentioned there, gitlab).

How do I get the runner registration working? It seems like I have to “convince” the gitlab-runner container to not use the public address for it’s POST requests, but I have no idea how to achive this.