Move the claimed-message notification loop out of the loop's pre-step
into Inbox.claim(target, turn), so the step-boundary operation publishes
its own claimed notifications like insertions and discards do.
Review finding (PR #791): the column carried bare values (no seq), so the
client could not seed its value store without risking a stale list block
outranking newer push frames — and nothing consumed the column at all,
leaving cold titles absent after a restart. SessionSummary.projections is
now the same SessionProjectionsBlock as the history tail (values +
asOfSeq; attached rows cut the live registry, cold rows serve the cache's
identity-checked cachedSnapshot whose asOfSeq is the lowest served-row
watermark). SessionManager.refreshList seeds each row's block into the
per-session projection store via per-key apply — partial-baseline
semantics: an absent key never clears, and higher-seq-wins keeps stale
list blocks beneath push frames and tail baselines — so cold titles
surface in the sidebar without opening a session.
SessionSummary grows an optional projections column (whole value per key,
same passthrough posture as the history-tail block): attached rows cut the
live registry watermark cache; cold rows view the persisted projection
cache's stored rows via the new registry viewCheckpoint face (version-
matching keys only, zero I/O) — the RFC's motivating scenario, every
session's title across a listing without loading one event log. The column
is fail-soft and absence-coded: no registry, no cache row, or a throwing
read serve the row without the column, never breaking the listing.