0.1.8 Beta2 CI: determinize recurring Windows Rust lifecycle fixtures #356

Problem

Hosted CI run 30904259353 on the exact #62 candidate b712be1021179c9d2415bef631bc8c1c466e0c0d failed Rust debug with two existing Windows lifecycle tests:

• proxy::tests::inspection_returns_when_a_descendant_inherits_output_handles — Gateway process inspection timed out.
• proxy::tests::restart_after_settings_port_change_stops_recorded_port_before_starting_new_port — Gateway did not become healthy within 20 seconds.

The PR changes are Python/docs/evidence-only; this is an independent Hosted test-fixture regression. The failure is a release blocker and must not be hidden by reruns.

Scope

• Add the narrowest test-only synchronization/control seam needed for these two fixtures.
• Keep production process inspection, Gateway lifecycle ownership, hard budgets, and fail-closed identity checks unchanged.
• Preserve real health/listener assertions where they are part of the behavior under test.
• Do not increase global or production timeouts, add retries, or skip tests.
• Reuse the proven patterns from closed CI: stabilize Windows process-inspection lifecycle tests on Hosted runners #298/Pass current-session identity through the Rust port-restart lifecycle test fixture #269/CI: make same-path Gateway upgrade fixture deterministic on Hosted Windows #299/test: stabilize same-path hosted lifecycle fixture #300 where applicable; do not duplicate a production fix.

Acceptance

• The two focused tests pass 10 consecutive runs in Rust normal and debug flavors.
• The complete Rust normal/debug matrix and Clippy pass on a new exact candidate without rerunning the failed job.
• No P0/P1/P2 review finding remains at the exact SHA.
• The change does not modify Python routing, catalog, tool compatibility, or release behavior.

Relationships

• Reproduced in 0.1.8 Beta2: Inventory Codex CLI 0.146 tool types and representative Responses lifecycles #62 candidate CI; blocks the Hosted gate for the current Beta2 campaign.
• Related prior deterministic fixture work: CI: stabilize Windows process-inspection lifecycle tests on Hosted runners #298, Pass current-session identity through the Rust port-restart lifecycle test fixture #269, CI: make same-path Gateway upgrade fixture deterministic on Hosted Windows #299, test: stabilize same-path hosted lifecycle fixture #300.
• This ticket does not change 0.1.8 Beta2: Inventory Codex CLI 0.146 tool types and representative Responses lifecycles #62 acceptance and does not unlock 0.1.8 Beta2: Define tool-type compatibility rules for custom Responses endpoints #65 by itself.

Verification-Class: strict