refactor(bottom-navigation): align with MD3 navigation behavior

Refactor BottomNavigation to improve Material Design 3 compliance, remove problematic children patterns, improve performance characteristics, and modernize the public API.

**Problems**

- Current API relies heavily on children composition in ways that are difficult to optimize
- Internal layout logic is tightly coupled to arbitrary child structures
- MD3 behaviors and visuals are not fully aligned with current Material guidelines
- Rendering performance can degrade in large lists or frequently updated screens
- Type safety and discoverability of the API can be improved
- The component has inconsistent behavior between platforms and edge cases

**Focus Areas**

- Improve active indicator implementation
- Improve shifting behavior
- Improve lazy screen rendering integration
- Improve badge handling

**Performance Opportunities**

- Reduce navigation item rerenders
- Improve animated transitions
- Optimize route updates

Start by locating the BottomNavigation implementation and its current API, then review how active indicators, shifting, lazy screen rendering, badges, and route updates are handled. Compare the existing behavior with the relevant Material Design 3 navigation guidance and identify the tests needed to define the refactor's completion criteria.

Written by the indexing model from the issue text.