fix: only nudge on explicit signed-out auth state

[paulcakeface]

Fixes #364.

The POSIX launcher previously treated every non-empty /auth.json body that was not signedIn:true as a confirmed signed-out state. That meant malformed, partial, or unrelated auth responses emitted the SessionStart sign-in warning and posted the sign-in nudge.

This change makes the shell path tri-state:

• signedIn:true -> quiet
• signedIn:false -> nudge
• anything else -> quiet

Regression coverage is added to the existing start-monk-agent-fastpath.sh test, which is already run by the repository's Ubuntu/macOS Install E2E job. The fixture exercises malformed, unrelated, explicit-false, and explicit-true payloads, and the test also asserts the three shipped POSIX launcher copies remain byte-identical.

Local validation:

• ./tests/start-monk-agent-fastpath.sh ✅
• ./tests/start-monk-agent-readiness-timeout.sh ✅
• ./tests/start-monk-agent-antigravity-python-path.sh ✅
• sh -n on all three POSIX launcher copies ✅
• generated-copy cmp checks ✅
• git diff --check ✅

Prepared with ChatGPT/Codex assistance.

[paulcakeface]

Bounty-deadline review nudge: this remains current against main and the focused launcher regression is green. If there’s anything you want changed before the 31 Aug submission cutoff, I can turn it around quickly.