The reasoning separation grew three files past their size ratchet. The Local
client's reasoning collector and the new separation helpers move to
local-reasoning.ts, the gateway client's thinking room and reply separation
become two private methods, and the Coach's error-code resolver moves out of
chat-bubble.tsx into coach-error-key.ts, still re-exported from
message-thread.tsx. Code motion apart from comments that said when a branch
was added rather than what it does. The baselines record the shorter files.
Refs #1276