docs: rewrite README to be more approachable and discoverable

[avivklas]

Summary

• Lead with the problem users actually search for: the Docker Hub toomanyrequests rate-limit error, followed by a short before/after example.
• Add badges, a table of contents, a numbered quick start (install → run → use), a comparison table against daemon.json registry-mirrors and manual rewriting, an FAQ, and a Contributing section.
• Move deep reference material (architecture diagrams, intercepted endpoints, context watching, crash recovery) under "How it works" further down. No content was dropped.

Fixes

• GitHub Action examples used fender-proxy/fender@v1, which doesn't exist as a tag; they now use @v0.3.2.
• Install section claimed "Requires Go 1.21+" while go.mod requires 1.26.6; it now points to go.mod and leads with prebuilt release binaries.

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