[chore] Refactor docker host connection verification

[guineveresaenger]

#697 enabled us to automatically fall back to the user socket for the docker host when running Docker locally. This change relies on a live connection verification using the native provider's configureDockerClient function.

This verification check should be more granular and more specifically scoped to local docker hosts, as we encountered #702 and #706 which affected SSH-based connections.

Additionally, we should ensure that the path of information is clear and look into a way to pass DOCKER_HOST to the bridged provider via configuration, not environment variables.