Surface a live "recovering…" status to chat clients during durable recovery #1620

Background

Follow-up to the deploy-churn recovery hardening (#1615, #1617, #1618, #1619).

When a chat turn is interrupted (deploy/eviction) and Think recovers it, there is
currently no client-facing "in progress" signal while recovery runs. The
client sees the partial transcript with no indication that the turn is being
recovered — it looks idle/stuck until recovery completes (or, now via #1619,
until a terminal error is replayed on connect).

#1619 fixed the terminal half (failed/exhausted turns are surfaced, and
replayed on reconnect — option "A", plus keeping benign skips silent, "C"). This
issue tracks the remaining progress half ("B"): show clients a
"recovering…" indicator so an interrupted-but-recovering turn reads as working
rather than frozen.

Why it's separate

Unlike #1619 (which reused the existing terminal MSG_CHAT_RESPONSE and needed
no client changes), a "recovering" indicator is a new client-facing
capability and spans multiple layers:

1. Protocol: a new chat message type (e.g. MSG_CHAT_RECOVERING) in
   agents/chat, broadcast on recovery detect/schedule and cleared on
   resolution.
2. Hydration: the status must be durable and replayed on connect (like the
   terminal status in Fix silent/frozen interrupted turns: replay terminal status on reconnect #1619), or a client that connects mid-recovery still sees
   nothing — this is the load-bearing requirement for the deploy/reconnect-storm
   case.
3. Debounce + reliable clear: recovery is detected many times under churn,
   so the signal must be idempotent (only on transition) and cleared on every
   terminal path (completed/failed/exhausted/skipped) or a spinner spins forever.
4. Client rendering: useAgentChat (and downstream SPAs) must render the
   new status; needs browser validation.

Acceptance

• A connected client shows a "recovering…" state for the duration of durable
  chat recovery, and a client that connects mid-recovery learns it on connect.
• The indicator clears on every terminal outcome; benign skips do not produce a
  stuck indicator.
• Backward-compatible: clients that don't understand the new signal ignore it.

Notes

Investigation + the A/B/C/D design options are written up in
examples/deploy-churn/INVESTIGATION.md (added in #1618).