Stabilize desktop and app integrations across startup, shutdown, and recovery

## Goal

Make supported app integrations, including Codex App and Claude Desktop surfaces, as reliable as the CLI paths.

## Problem

Desktop applications have longer lifetimes, multiple subprocesses, background requests, signed application bundles, and crash/restart behavior that differ from one-shot CLIs. A successful launcher smoke test is not enough to claim stable protection.

## Acceptance criteria

- Test clean startup, failed startup, normal exit, forced termination, gateway crash, app crash, and machine restart recovery.
- Ensure temporary provider/settings changes are scoped to the protected session and restored atomically.
- Verify local conversations separately from remote/cloud tasks.
- Capture background, utility, file, image, tool, and streaming requests that belong to supported surfaces.
- Detect unprotected subprocesses or traffic and report them clearly.
- Prevent orphan gateways, stale backups, duplicated providers, and broken unprotected app startup.
- Add platform-specific release E2E for signed or packaged apps where automation permits.
- Publish an evidence-based support matrix and label unverified surfaces as unverified.

Start with the existing launcher smoke test and inventory the supported Codex App and Claude Desktop integration paths, including startup, shutdown, crash, and restart recovery. Build the acceptance-test matrix for local versus remote tasks and supported request surfaces; done requires evidence for each scenario, clear detection of unprotected work, and a published support matrix marking unverified surfaces.

Written by the indexing model from the issue text.