Factorize get_docker_client function

[cbeauchesne]

Motivation

Preparation for #5581

Changes

Workflow

1. ⚠️ Create your PR as draft ⚠️
2. Work on you PR until the CI passes
3. Mark it as ready for review
   • Test logic is modified? -> Get a review from RFC owner.
   • Framework is modified, or non obvious usage of it -> get a review from R&P team

🚀 Once your PR is reviewed and the CI green, you can merge it!

🛟 #apm-shared-testing 🛟

Reviewer checklist

• If PR title starts with [<language>], double-check that only <language> is impacted by the change
• No system-tests internal is modified. Otherwise, I have the approval from R&P team
• A docker base image is modified?
  • the relevant build-XXX-image label is present
• A scenario is added (or removed)?
  • Get a review from R&P team

[github-actions]

CODEOWNERS have been resolved as:

utils/_context/docker.py                                                @DataDog/system-tests-core
utils/_context/_scenarios/docker_ssi.py                                 @DataDog/system-tests-core
utils/_context/_scenarios/endtoend.py                                   @DataDog/system-tests-core
utils/_context/_scenarios/parametric.py                                 @DataDog/system-tests-core
utils/_context/containers.py                                            @DataDog/system-tests-core
utils/k8s/k8s_component_image.py                                        @DataDog/system-tests-core
utils/scripts/get-image-list.py                                         @DataDog/system-tests-core