fix: restart Windows companion when launch client changes

[ceodaradigu]

Fixes #272.

What changed

• persist the detected Windows launch client in the companion state file
• include that value in the healthy-process reuse gate
• keep all three shipped PowerShell launcher copies byte-identical
• add an isolated Codex-to-Cursor drift regression and run it in Windows Install E2E

Why

The Windows launcher exports MONK_AGENT_LAUNCH_CLIENT only when it spawns the companion. Its state fingerprint omitted that value, so a healthy process started by Codex was reused when Cursor later invoked the launcher. The process therefore retained stale codex attribution.

Impact

Changing host clients now causes one intentional restart so the companion inherits accurate client attribution. Subsequent launches from the unchanged client continue to use the existing fast path.

Validation

launch_client_restart_status=pass launches=2

The regression proves the initial Codex launch, unchanged reuse, a single restart after switching to Cursor, persisted launch_client=cursor state, and byte-identical generated launcher copies. It is wired into .github/workflows/install-e2e.yml. git diff --check also passes.

The pre-existing start-monk-agent-readiness-timeout.ps1 harness reached the expected 2-second launcher error but still reports its known Windows test-harness ExitCode issue; this patch does not touch that path.

[ceodaradigu]

@nooga This report and fix are ready for bounty review before the current contest deadline. It reproduces cross-client launch attribution drift and adds a focused Windows regression. The current head (d463eb6) is mergeable, with local result launch_client_restart_status=pass launches=2, and all three shipped launcher copies remain byte-identical. Please let me know if any additional eligibility evidence is needed; no merge or credit is assumed.

[nooga]

Thanks for digging into this.

MONK_AGENT_LAUNCH_CLIENT is deliberately excluded from the healthy-process restart gate — commit 702884c documents that. It's there so the companion doesn't restart every time you switch between agents in the same session. Re-adding it on Windows only would reintroduce exactly that churn, and asymmetrically.

Closing; #272 is flagged for a maintainer call on whether there's a narrower version of the problem worth fixing.