feat(backend): add FastAPI service

[gac0812]

Summary

• add the FastAPI service under backend/
• include API health testing, environment defaults, and quality-tool configuration
• add repository ignore rules for Python and Expo generated files

Validation

• uv run pytest
• uv run ruff check .
• uv run mypy

[fennoai]

Review Summary

Found one maintainability issue in the test dependency setup. The health test, Ruff, mypy, locked sync, and package build otherwise completed successfully.

View job run

[fennoai]

[P3] Use the supported Starlette test-client dependency

The locked Starlette 1.3.1 prefers httpx2, so the current httpx dependency makes every test run emit StarletteDeprecationWarning; it also fails collection when warnings are treated as errors. Replacing this with httpx2 and refreshing uv.lock removes the warning and keeps the test setup forward-compatible.

[gac0812]

Fixed in gac0812@ae56f1d. Replaced the deprecated httpx test dependency with httpx2 and refreshed uv.lock. Verified Ruff, formatting, mypy, and uv run pytest -W error (1 passed with no warning).