fix: assert HED routes by reaching them, not by reading app.routes

[neuromechanist]

develop and every open PR are red on one test, and it is not any of their
faults.

test_hed_routes_mounted does [r.path for r in app.routes]. Starlette 1.x
puts _IncludedRouter objects in app.routes for anything added via
include_router, and those have no .path, so the comprehension raises
AttributeError. CI installs unlocked (uv pip install --system -e ".[dev]"), so
it resolved starlette==1.6.0 / fastapi==0.141.1 while uv.lock pins
starlette==0.50.0 / fastapi==0.128.0. The break arrived from upstream with no
change in this repo.

The app is fine

Worth stating first, because an AttributeError in a route-mounting test looks
alarming. Verified directly under fastapi==0.141.1 / starlette==1.6.0:

introspection FAILS: '_IncludedRouter' object has no attribute 'path'
route types: ['APIRoute', 'Mount', 'Route', '_IncludedRouter']
  /hed/ask      -> HTTP 422   (route exists, rejected an empty body)
  /hed/sessions -> HTTP 200

The routes are mounted and serving. Only the test was wrong: it asserted a
framework internal rather than the property its own docstring names.

The fix

Reach the three routes and require that none answers 404, which is the only
status that means "not mounted" -- a 422 is the route rejecting an empty body, and
a 405 would be a method mismatch; both are mounted. That assertion cannot break on
the next internals rename, which is the actual lesson here.

The sibling test at line 55 introspects a raw APIRouter and is untouched: those
routes still carry .path under both versions, so it keeps its stronger
exact-path assertion.

Verified under both majors

• Locked (starlette 0.50.0): 36 passed
• CI's resolution (starlette 1.6.0): 36 passed

Not in scope

Two other CI jobs fail for unrelated reasons, and I left both alone:

• Build and Test Docker Image -- the Dockerfile's apt-get step installing the
  GitHub CLI keyring exits 100. An apt/upstream-repo problem, not Python.
• claude-review -- the action itself errors with "Internal error: directory
  mismatch for directory .../tsconfig.json".

Worth separate issues if they persist.

Related: #352 is blocked on this one.