Preserve replies when terminal chat persistence fails

[hamzamerzic]

Summary

• atomically materialize any saved live assistant before clearing a wedged run
• append a durable resumable interruption marker when no reply was saved
• preserve queued messages and unanswered question cards during recovery
• fence cleanup by run identity so a stale recovery cannot overwrite a newer turn

Context

This hardening was discovered while testing #277. That PR should still normalize its typed image path at the provider boundary; this change independently guarantees that a future terminal persistence failure cannot clear the only recovery handle and leave a silent user-to-user gap.

Tests

• MOBIUS_TEST_RUNTIME=1 python3 -m pytest -q backend/tests/test_wedged_marker_sweep.py backend/tests/test_chat_writer_contention.py::test_stale_wedged_recovery_cannot_clobber_new_run (13 passed)
• python3 -m py_compile backend/app/chat.py backend/app/chat_writer.py

[hamzamerzic]

Merged to main as part of #304, including the reviewed terminal-persistence recovery and its integration coverage. Closing this now-superseded source PR.