docs: unify README with the shared skeleton and expand the org profile

[DerekCorniello]

Part of muxlang/mux-context#14.

Two different jobs here, so two different treatments:

• README.md (this repo's own) gets the shared skeleton like the code repos: centered logo + title + tagline, badge row, --- dividers, Related repositories table, License/maintainer footer.
• profile/README.md is the org front door at github.com/muxlang, not a repo README. It keeps the shared visual identity but gets a landing-page treatment: a first-taste code sample, install + playground calls to action, why-Mux highlights, and the repo map.

Making the profile byte-identical to a library README would undersell the one page that should be the most expressive, so "unify" here means shared chrome across the library repos plus a more editorial profile.

The code sample is lifted from the mux-compiler README so it is known-valid Mux.

🤖 Generated with Claude Code

[greptile-apps]

Greptile Summary

This PR gives both READMEs a shared visual identity (centered logo, badge row, --- dividers, Related repositories table) while keeping the org profile (profile/README.md) intentionally more editorial than a standard library README.

• README.md gains a structured inventory table, a "How syncing works" section, a Related repositories table, and a license/maintainer footer — all content that was either missing or buried in prose.
• profile/README.md is promoted to a proper landing page with a code sample (lifted from mux-compiler README), install + playground calls to action, and a "Why Mux?" highlights list, while the Playground badge now correctly targets /playground (distinct from the Website badge).
• The HTML <div align="center"> blocks are properly opened and closed in both files, and all badge destination URLs are unique and point to meaningful targets.

Confidence Score: 5/5

Documentation-only changes with no code logic; both files are structurally sound and ready to merge.

Both files are pure Markdown with no executable logic. HTML tags are balanced, badge URLs are distinct and point to meaningful targets, and the code sample in the profile is stated to be lifted from the already-reviewed mux-compiler README. Nothing here can break a build or introduce a runtime regression.

No files require special attention.

Important Files Changed

Filename	Overview
README.md	Adds centered logo + badge header, converts bullet-list inventory to a table, adds "How syncing works" section and a Related repositories table with a license footer — purely additive documentation improvements, no logic changes.
profile/README.md	Expands org landing page with centered hero, four distinct badge links (Website, Docs, Playground, License), a first-taste code sample, install snippet, "Why Mux?" highlights, and a tightened "Getting involved" section — editorial content only, no code logic.

_{Reviews (2): Last reviewed commit: "docs: point the playground badge at the ..." | Re-trigger Greptile}

[DerekCorniello]

Triage of the two findings:

1. Duplicate badge destination — valid, fixed. The Website and Playground badges both pointed at the site root. There is a distinct playground route (src/pages/playground.tsx, and https://mux-lang.dev/playground returns 200), so the Playground badge and the inline "try it" link now point there.

2. Sonar badge — not applying. Flagged as possibly unregistered. Verified against the live endpoint instead of assuming: sonar-project.properties sets sonar.projectKey=muxlang_.github, this repo runs .github/workflows/sonar.yml, and the badge endpoint returns HTTP 200 rendering "quality gate passed". The badge resolves.

[sonarqubecloud]

Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
0.0% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud