modernize FastAPI stack

[rednafi]

Summary

• Merge the approved pwdlib PR locally, then modernize the app around the current FastAPI docs stack.
• Move runtime dependencies to fastapi[standard], PyJWT, pwdlib[argon2], and pydantic-settings.
• Drop Python 3.11/3.12 support and keep the active matrix on Python 3.13 and 3.14.
• Update Dockerfiles, compose, CI actions, Dependabot cadence, tests, and README claims to match the new runtime.

Validation

• uv run --python 3.14 pytest -vv
• uv run --python 3.13 pytest -vv
• make test
• make lint-check
• uv lock --check
• uv build
• docker build -f dockerfiles/python313/Dockerfile -t fastapi-nano:py313 .
• docker build -f dockerfiles/python314/Dockerfile -t fastapi-nano:py314 .
• Standalone container smoke tests for py313 and py314: /docs, /, /token, /api_a/22, /api_b/22
• docker compose up -d --build
• Compose/Caddy smoke tests: /docs, /, /token, /api_a/22, /api_b/22, CORS preflight

Notes

The compose stack was left running locally after verification on http://127.0.0.1:5002.