fix(sessions): read the composer from a styled capture so a prompt suggestion is not a draft

Claude Code draws its prompt suggestion in an empty composer, the first letter in the reverse-video cursor cell and the rest faint, so a plain capture read it as typed text and keep-warm never nudged those sessions. The keep-warm pane read now uses capture-pane -e and drops the suggestion before checking the composer.

Also from review: an off status carries no window, automation and an unreadable composer retry instead of stopping, a failed evaluation re-arms a retry, a trigger during an evaluation queues one follow-up that remove() cancels, and the cap's clock is seeded from lastSubmitAt for pre-upgrade state.

src/session.ts

@@ -1001,8 +1001,9 @@ export class Session extends EventEmitter {
     // response viewer re-derive the live conversation without waiting for the
     // user to type again.
     this._lastSubmitAt = config.lastSubmitAt ?? 0;
-    // Restored so a restart neither reopens the keep-warm window nor drops the choice.
-    this._lastRealPromptAt = config.lastRealPromptAt ?? 0;
+    // Restored so a restart neither reopens the keep-warm window nor drops the choice. A state.json
+    // from before the field has only `lastSubmitAt`, and every submit then was a real one.
+    this._lastRealPromptAt = config.lastRealPromptAt ?? config.lastSubmitAt ?? 0;
     this._keepWarmEnabled = config.keepWarmEnabled;
     // Restored chain: its tail is the conversation the CLI was actually on when
     // the server stopped, which outranks the launch id seeded just above. The