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/web/routes/session-routes.ts

@@ -1228,6 +1228,11 @@ export function registerSessionRoutes(
     const activeId = await resolveActiveClaudeSessionIdFromHistory(session, projectsDir);
     if (activeId && activeId !== session.claudeSessionId) {
       session.adoptClaudeSessionId(activeId);
+      // Flush the Enter that vouched for this adoption to state.json. A `/clear`
+      // emits no completion event, so without this the anchor could still be
+      // unpersisted when the server restarts — and recovery would fall back to
+      // the launch conversation.
+      ctx.persistSessionState(session);
       // Docker sessions: keep the case's resume seed following the live conversation.
       if (session.docker) {
         void persistDockerCaseClaudeSessionId(CODEMAN_CONFIG_DIR, session.docker.containerName, activeId).catch(

src/web/server.ts

@@ -2464,6 +2464,10 @@ export class WebServer extends EventEmitter {
               envOverrides: savedEnvOverrides,
               effort: savedState?.effort,
               attachmentHistory: savedAttachmentHistory,
+              // The pane's last Enter. Without it the response viewer would show
+              // the launch conversation until the user types again, even though
+              // the re-attached CLI is on a post-`/clear` one.
+              lastSubmitAt: savedState?.lastSubmitAt,
               // Remote SSH metadata must round-trip on recovery: without it the
               // attach cwd falls back to the (nonexistent-locally) remote path and
               // respawn rebuilds a LOCAL command, breaking the pane and silently