fix(cockpit): fix chat/input and chat/threads production builds (#77) #269

Job	Run time
Cockpit — build / test	1m 21s
Website — e2e	2m 9s
Cockpit — deploy smoke dry-run	1m 16s
Cockpit — secret-gated integration	1m 16s
Library — lint / test / build	1m 29s
Cockpit — build all examples	4m 24s
Website — lint / build	1m 42s
Cockpit — e2e	2m 3s
MCP — build / smoke	1m 7s
Cockpit — representative capability smoke	1m 13s
Chat Agent — smoke	1m 24s
Deploy → Vercel	5m 15s
Production smoke	4m 46s
	29m 25s

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