fix(web): keep the viewer's conversation anchor across a Codeman restart

start() reassigns _claudeSessionId to `resumeSessionId || id` on every launch,
including the path that re-attaches to a mux session that outlived the restart.
A pane whose CLI had moved on via /clear therefore came back pointing the
response viewer at its pre-/clear transcript, and because Session.lastSubmitAt
lived only in memory, the history correlation had nothing to correct it with
until the user happened to type again — observed as hours of the eye showing a
conversation the pane had long since left.

Persist lastSubmitAt in SessionState, restore it in restoreMuxSessions(), and
flush it when the viewer adopts (a /clear emits no completion event, which is
the trigger that would otherwise have persisted it). Recovered panes now
re-derive their live conversation on the viewer's first poll.

Restoring a stale anchor is safe: the resolver already refuses a candidate
transcript older than the one the pane is currently on, which is the shape of a
respawn into a fresh conversation.

.changeset/fix-claude-viewer-session-pin.md

@@ -12,3 +12,11 @@ was typed into last — and the adoption was written back to the session, so the
 mispin persisted. Entries are now credited to a pane only when they land within
 10s of that pane's own Enter and no other pane on the cwd submitted closer, the
 same last-submit correlation the Codex locator already uses.
+
+That correlation also has to survive a restart. `start()` resets
+`claudeSessionId` to the launch id even when re-attaching to a mux session whose
+CLI has since moved on via `/clear`, so a recovered pane pointed the viewer at
+its pre-`/clear` transcript — and with the anchor itself living only in memory,
+nothing corrected it until the user happened to type again. `lastSubmitAt` is
+now persisted in `SessionState` and restored on boot recovery, so the viewer
+re-derives the live conversation on its first poll.