docs: modernize README with clean hero, client badges, and native mermaid architecture - #16

Node.js 20 is deprecated. The following actions target Node.js 20 but are being forced to run on Node.js 24: actions/checkout@v4, astral-sh/setup-uv@v5. For more information see: https://github.blog/changelog/2025-09-19-deprecation-of-node-20-on-github-actions-runners/