Generate FastAPI Code Documentation

Please can you:

1. Review the Python modules in /backend/app/
2. Create documentation pages in /docs/docs/code/fastapi/ for each module
3. Use mkdocstrings syntax (::: app.module_name) to auto-generate docs from docstrings
4. Create an index.md with links to all module pages
5. Update the /docs/mkdocs.yml navigation to include all FastAPI modules under Code Documentation → Backend

Each module page should follow this format:

# Module Name

::: app.module_name

For schemas, include both auth and letters submodules in a single schemas.md file.