## Description
Base installs without the `proxy` extra crash during CLI command
registration because `headroom.proxy.request_scope` imported FastAPI at
module import time. That import is only needed for typing on
`normalize_request_path`.
This change keeps the FastAPI `Request` import under `TYPE_CHECKING` so
the CLI path used by `headroom --help` no longer requires FastAPI.
Closes#2561
## Type of Change
- [x] Bug fix (non-breaking change that fixes an issue)
- [ ] New feature (non-breaking change that adds functionality)
- [ ] Breaking change (fix or feature that would cause existing
functionality to not work as expected)
- [ ] Documentation update
- [ ] Refactoring (no functional changes)
- [ ] Performance improvement
- [ ] Test update
- [ ] Build/CI change
- [ ] Other (please describe):
## Changes Made
- Make the FastAPI `Request` import type-checking only in
`headroom/proxy/request_scope.py`
- Add a subprocess regression test that imports `request_scope` and
`project_context` with FastAPI blocked and verifies
`normalize_scope_path`
## Testing
### Test commands run
```bash
PYTHONPATH=. python3 -m pytest tests/test_proxy_request_scope.py tests/test_request_scope_no_fastapi.py -q
ruff format --check headroom/proxy/request_scope.py tests/test_request_scope_no_fastapi.py
ruff check headroom/proxy/request_scope.py tests/test_request_scope_no_fastapi.py
```
### Test Output
```text
========================= 5 passed, 1 warning in 0.93s =========================
2 files already formatted
All checks passed!
```
## Real Behavior Proof
### Environment
- Linux x86_64, Python 3.11.15
- Shallow sparse checkout of headroom main at commit parent of this PR
- System/Hermes venv Python with pytest and ruff available
### Exact command
```bash
PYTHONPATH=. python3 - <<'PY'
import builtins, sys
real = builtins.__import__
def imp(name, *a, **k):
if name == "fastapi" or name.startswith("fastapi."):
raise ModuleNotFoundError("No module named 'fastapi'")
return real(name, *a, **k)
builtins.__import__ = imp
import headroom.proxy.request_scope as rs
import headroom.proxy.project_context as pc
rs.normalize_scope_path({"path": "/a"}, "/b")
print("ok", "fastapi" not in sys.modules, hasattr(pc, "with_project_prefix"))
PY
```
### Observed result
```text
ok True True
```
Importing the request-scope helpers no longer requires FastAPI, and
scope path normalization still works.
### Not tested
- Full base `pip install headroom-ai` (no extras) end-to-end on a clean
venv without the monorepo source tree
- Full monorepo `make ci-precheck` / cargo workspace
- Live proxy traffic or FastAPI request path behavior beyond the
existing unit test for `normalize_request_path`
## Review Readiness
- [x] I have tested these changes locally
- [x] I have added/updated tests where applicable
- [x] I have updated documentation if needed (N/A)
- [x] My code follows the project's style guidelines
- [x] I have run linting/formatting checks
- [x] I have considered security implications
- [x] This PR is ready for review
