fix(tui): survive dead terminal during shutdown #2015

Job	Run time
Static checks	1m 20s
Inspector handoff (ubuntu-latest)	47s
Terminal tools (ubuntu-latest)	37s
Test (coding-agent 1/3)	5m 16s
Inspector handoff (macos-latest)	1m 2s
Terminal tools (macos-latest)	1m 1s
Test (coding-agent 2/3)	5m 15s
Test (coding-agent 3/3)	5m 10s
Terminal tools (windows-latest)	1m 32s
Inspector handoff (windows-latest)	1m 38s
Test (workspaces + scripts)	3m 57s
Check and test	5s
	27m 40s

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