[business_analysis] Operator credentials roster UX fixes at scale

_Automatically composed from the parent epic at dispatch time._

PRD settled: 7 roster-at-scale items in scope with oracles (stored has-secret flag, keyset + 10,000+ cap, trigram/operator search, async multi-owner, server tree, all-or-nothing bulk ≤10k, stored health data). Depends on 9378 merging. Memory: none applied.