docs: update differentiable economics lectures and fix typos (#409)

- Rewrite overview sections for differentiable_dynamics and differentiable_filters
  with richer motivation and clearer learning objectives
- Add bibliography entries (Jovanovic 1979, 1982; Moscarini 2005)
- Fix typos: ie.. → i.e., inplace → in-place, cholesky → cholesky!,
  plural/article errors, double spaces, awkward phrasing
- Update Manifest.toml

Co-authored-by: Claude Opus 4.6 <noreply@anthropic.com>

Author: jlperla