Running action inside container without docker daemon fails

[amaschas]

Description

I'm using the example configuration from https://github.com/docker/build-push-action?tab=readme-ov-file#git-context with one modification: I'm running a custom container without an installed docker daemon inside the github runner:

jobs:
  docker:
    runs-on: ubuntu-latest
    container: <custom_container>
    steps:
      -
        name: Login to Docker Hub
        uses: docker/login-action@v3
        with:
          username: ${{ vars.DOCKERHUB_USERNAME }}
          password: ${{ secrets.DOCKERHUB_TOKEN }}
      -
        name: Set up Docker Buildx
        uses: docker/setup-buildx-action@v3
      -
        name: Build and push
        uses: docker/build-push-action@v6
        with:
          push: true
          tags: user/app:latest

In this the docker/setup-buildx-action and docker/build-push-action will succeed, because they can apparently communicate with the docker daemon on the host, but docker/login-action fails because it can't find a docker executable on the container. I would expect the docker/login-action to work like the others, employing the hosts docker daemon to execute the login command.