Stabilize remote routing e2e tests

[starr-openai]

Stack:

• PR #22199 Isolate tmp-dependent tests from ambient git
• PR #22201 Use remote fs for turn diff repo root
• PR #22200 Emit unified exec end on startup failure
• PR #22202 Stabilize remote routing e2e tests

Summary:

• keep local and remote environments addressable in remote-aware test builders
• wait for routed function-call output instead of assuming turn completion ordering
• keep unrelated network-denial coverage on the local test path

Testing:

• Not run locally; relying on CI for this Codex PR.