test: isolate runtime state and PTY integration

[Lint111]

Summary

• Give the quick-start API suite its own temporary HOME.
• Install a suite-wide temporary HOME / USERPROFILE and explicit VITEST
  marker before application imports can resolve runtime paths.
• Preserve the platform Playwright browser cache while isolating all Codeman
  state, then restore the caller environment and remove only the temporary
  fixture directory during teardown.
• Attach a deterministic live echo PTY during Vitest runs and skip real
  tmux/agent geometry calls, so integration tests exercise input/output without
  creating or controlling host sessions.

Root cause

The test harness did not reliably identify itself as a test environment and
allowed module-level paths to resolve from the developer's real home directory.
The quick-start suite could therefore clean up the real
~/codeman-cases/testcase directory, including the checkout running Vitest.
Session integration tests could also launch real tmux/agent processes.

Scope

This is the test-infrastructure slice extracted from #173. It changes the
quick-start fixture, global test setup, and a VITEST-guarded session adapter.
Normal application execution is unchanged.

Validation

• npm run test:ci -- test/quick-start.test.ts test/integration-flows.test.ts:
  2 files, 23 tests passed
• Working tree and git diff --check: clean