Improve multi-client discovery and server UX

[SegfaultSorcerer]

Summary

• improve client discovery and config metadata across Claude, Codex, Cursor, Windsurf, and VS Code
• add transparent TOML rewrite support, better playground filtering, and more robust proxy health/test flows
• simplify the Servers UI with a dedicated detail panel, collapsible setup status, and persistent per-server logs

Testing

• cargo test -p conduit -- --test-threads=1
• cargo check -p conduit
• npm run build
• npm run lint