Fix Starlette 1.0.0 compatibility in TemplateResponse calls (#64116)

[syhstanley]

Starlette 1.0.0 removed the deprecated `TemplateResponse(name, context)`
signature where `request` was passed inside the context dict. This caused
the API server to crash with `TypeError: unhashable type: 'dict'` (HTTP 500)
whenever the SPA catch-all route or the simple auth manager UI was served.

Root cause: Both `core_api/app.py` and `simple_auth_manager.py` were
using the old signature:

# Old (broken on starlette 1.0.0)
templates.TemplateResponse(
    "/index.html",
    {"request": request, "backend_server_base_url": ...},
)

Fix: Update to the current signature (supported since starlette 0.27.0,
so fully backward-compatible with our `>=0.45.0` minimum):

# New (works on starlette 0.45.0 – 1.0.0+)
templates.TemplateResponse(
    request,
    "/index.html",
    {"backend_server_base_url": ...},
)

Also removes the temporary `starlette<1` upper bound added in #64115 and
its associated comment.

Tested locally with starlette 1.0.0:

• airflow-core/tests/unit/api_fastapi/execution_api/test_app.py — 7/7 passed (includes the previously failing test_access_api_contract)
• airflow-core/tests/unit/api_fastapi/auth/managers/simple/ — 202/202 passed
• airflow-core/tests/unit/api_fastapi/core_api/test_security.py + auth routes — 89/89 passed

closes: #64116

---

Was generative AI tooling used to co-author this PR?

• Yes (Claude Code)

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