start docker container from within self hosted bitbucket pipeline (dind) - docker

Question

I work on a spring-boot based project and use a local machine as test environment to deploy it as a docker container.
I am in the middle of creating a bitbucket pipeline that automates everything between building and deploying. For this pipeline I make use of a self hosted runner (docker) that also runs on the same machine and docker instance where I plan to deploy my project.
I managed to successfully build the project (mvn and docker), and load the docker image into my GCP container registry.
My final deployment step (docker run xxx, see yml script below) was also successful but since it is running in a container itself it was not running the script on the top level docker.
as far as I understand the runner itself has access to the host docker, because the docker.sock is mounted. but for each step another container is created which does not have access to the docker.sock, right? So basically I need to know how to give access to this file unless there's a better solution to that.
here the shortened pipeline definition:
image: maven:3.8.7-openjdk-18
definitions:
services:
docker:
image: docker:dind
pipelines:
default:
# build only for feature branches or so
branches:
test:
# build, docker and upload steps
- step:
name: Deploy
deployment: test
image: google/cloud-sdk:alpine
runs-on:
- 'self.hosted'
- 'linux'
caches:
- docker
script:
- IMAGE_NAME=$BITBUCKET_REPO_SLUG
- VERSION="${BITBUCKET_BUILD_NUMBER}"
- DOCKER_IMAGE="${DOCKER_REGISTRY}/${IMAGE_NAME}:${VERSION}"
# Authenticating with the service account key file
- echo $GCLOUD_API_KEYFILE > ./gcloud-api-key.json
- gcloud auth activate-service-account --key-file gcloud-api-key.json
- gcloud config set project $GCLOUD_PROJECT
# Login with docker and stop old container (if exists) and run new one
- cat ./gcloud-api-key.json | docker login -u _json_key --password-stdin https://eu.gcr.io
- docker ps -q --filter "name=${IMAGE_NAME}" | xargs -r docker stop
- docker run -d -p 82:8080 -p 5005:5005 --name ${IMAGE_NAME} --rm ${DOCKER_IMAGE}
services:
- docker