Fixes the account-sync wedge filed by multis (docs/01-product/beeperbox-asks/account-sync-resilience.md): a WhatsApp account added via noVNC didn't surface, and a plain docker restart didn't recover it — it self-corrected only later.

Root cause (debug-method, evidence-grounded)

getAccountMap() — the accountID → network map every chat verb uses for network labels — cached its result for the whole process lifetime with no TTL and no invalidation (if (accountCache) return accountCache;), and happily froze an empty map captured during the backend's post-restart sync window (when /v1/accounts briefly returns []).

Consequences, all matching the report:

• A runtime account-add rendered network:"unknown" in every chat verb until the MCP process restarted.
• A cold cache populated during the sync window froze empty for the whole run → a plain docker restart re-poisoned it from a still-syncing backend → wedge survived, recovering only on a luckier restart / full down+up.

list_accounts itself is stateless (live read), so its 0 was the backend's transient empty during sync — relayed silently, indistinguishable from "no accounts." The backend's per-account status field was dropped entirely.

Fix

• Bound the cache: TTL BEEPERBOX_ACCOUNT_CACHE_TTL_MS (default 60s; 0 = always live) and never cache an empty result — served for the one call that saw it, re-read next call, so the map self-heals the instant Beeper finishes syncing. Runtime account-add now reflected within the TTL, no restart.
• Surface status on list_accounts (connected/connecting/… — new schema field) so a syncing bridge ≠ a missing account.
• Observability: stderr WARN when /v1/accounts returns 0, instead of silently relaying an ambiguous empty list.

Verification

• 4 new unit tests, each written to fail against the old unbounded cache (watched fail → 3 fail/1 guard, then implemented → all pass). 48/48 green.
• Live-validated against the running container: list_accounts returns status for all 5 accounts (WhatsApp incl.); list_inbox resolves 0 unknown-network chats.
• Docs updated: beeperbox.context.md schema + retry guidance, docs/PRD.md env table.

Acceptance (from the ask)

• ✅ backend healthy with N accounts → list_accounts returns N (live read).
• ✅ add/remove account reflected without a full teardown (within TTL; list_accounts instant).
• ✅ divergence is logged, not silent.
• ✅ a docker restart recovers a wedged relay (empty is never frozen).

Healthcheck left unchanged on purpose — failing it on 0 accounts would wedge first-run/fresh-login containers (legitimately 0) and the release gate; the stderr WARN is the observability path instead.

Release scope: MINOR (new status schema field) when cut.

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