feat: add animated sidebar

[starc007]

What changed

• add a composable Animated Sidebar with desktop icon-rail collapse and a focus-managed mobile sheet
• morph the desktop sidebar width with a spring while keeping icons aligned and labels unstretched
• add shared-layout hover and active backgrounds, a panel-style toggle icon, profile footer, and reference-aligned preview styling
• add composable nested navigation primitives with parent-only carets, top-origin morphing, staggered submenu items, and collapsed-rail handling
• update registry metadata, component dates, agent documentation, and focused sidebar tests

Why

The sidebar needed to behave like a true application sidebar rather than a drawer, with polished open/close motion, stable icon alignment, mobile support, and production-ready nested navigation.

Validation

• bun run check
• bun test — 64 passing
• git diff --check
• visual verification in the local component preview