Add Docker CI rollout baseline

[ohmyfelix]

What changed

• Add the Dockette Docker workflow with Test, Build, and Docs jobs.
• Add mailx-style Makefile baseline targets for build, smoke test, and run.
• Normalize README badges to the copybara style and keep Maintenance guidance.
• Add repo-local AGENTS.md and CLAUDE.md instructions.

Why

• Establish the Dockette CI rollout baseline for the nginx image with consistent badges, commands, and automation.