Split Makefiles into separate files and add clean target

What does this MR do and why?

To allow easier growth for linting and tests, split up Makefiles in the style adopted in GDK: https://gitlab.com/gitlab-org/gitlab-development-kit/-/tree/main/support/makefiles?ref_type=heads.

How to set up and validate locally

Numbered steps to set up and validate the change are strongly suggested.

  1. Configure a local GitLab Docs environment: https://gitlab.com/gitlab-org/technical-writing-group/gitlab-docs-hugo/-/blob/main/doc/setup.md.
  2. Check out this branch.
  3. Run make all && make view. Test should pass and Hugo should launch a preview.

Merge request acceptance checklist

This checklist encourages us to confirm any changes have been analyzed to reduce risks in quality, performance, reliability, security, and maintainability.

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