[business_analysis] Fix October broken sessions root causes

_Automatically composed from the parent epic at dispatch time._

PRD settled: 9 of 10 fix asks in scope, each with a test oracle that fails on develop today (5a and 5b reproduced). 1c already shipped in Task 9264 (tests pass). New causes: stalled and client_unsupported (terminal). The 5-day prod check runs after deploy. Memory: none applied.