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.

src/types/session.ts

@@ -459,6 +459,15 @@ export interface SessionState {
   effort?: EffortLevel;
   /** Sanitized per-session attachment history. */
   attachmentHistory?: SessionAttachmentHistoryItem[];
+  /**
+   * Wall-clock ms of this pane's last Enter (Session.lastSubmitAt). Persisted
+   * because it is the response-viewer's only anchor for re-deriving the pane's
+   * live conversation after a Codeman restart: `start()` resets
+   * `claudeSessionId` to the launch id even when re-attaching to a mux session
+   * whose CLI has since moved on via `/clear`, and the correlation cannot run
+   * again until the pane's own Enter is known.
+   */
+  lastSubmitAt?: number;
   /**
    * PTY-exit circuit breaker tripped — respawn blocked until an explicit restart
    * (COD-118). Runtime-only: never restored on boot (fresh server = fresh breaker).