test(main): fix route-registration tests for FastAPI >=0.138

[timothybrown]

Problem

The backend Dependabot PRs (#33 starlette, #36 pydantic-settings) fail CI on two tests:

tests/test_main.py::TestAppRoutes::test_api_routes_registered     - AttributeError: '_IncludedRouter' object has no attribute 'path'
tests/test_main.py::TestAppRoutes::test_websocket_route_registered - AttributeError: '_IncludedRouter' object has no attribute 'path'

Root cause

This is not a problem with either dependency. CI installs the backend with uv pip install -e ".[dev]", which ignores uv.lock and resolves fresh from PyPI — so it picks up FastAPI 0.138.x. In 0.138, include_router() no longer flattens sub-routes into app.routes; instead it inserts opaque _IncludedRouter wrapper objects that have no .path. The tests did [r.path for r in app.routes], which now throws.

Because the backend Dependabot PRs trigger backend CI (path-scoped), they surface the failure; main would fail the same way if its backend CI re-ran.

Fix

Assert against public, version-stable APIs instead of FastAPI's internal route objects:

• HTTP routes → app.openapi()["paths"]
• WebSocket route → app.url_path_for("websocket_live") (WebSockets aren't in the OpenAPI schema)

Deliberately avoids the private _IncludedRouter / effective_route_contexts internals — depending on those is what made the test brittle in the first place.

Verification

• ✅ Full backend suite (251 tests) passes on FastAPI 0.138.1 (the version CI resolves)
• ✅ test_main.py passes on the locked FastAPI 0.135.3 / Starlette 1.0.1
• ✅ ruff clean

Once merged, #33 and #36 just need a rebase to go green.

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