Carry conversations into new sessions with a visible summary

- Bots get continue_in_new_session: the bot writes a title and summary,
  the session closes for good (read-only) and the new one opens with the
  summary as a "Carried over from the last session" message that links
  back to the old session.
- Continue in new session (conversation menu, sessions modal) and the
  automatic rollover at the session length do the same; New session now
  starts a fresh, unlinked session.
- Session length is an app setting in Settings > General.
- ?session_id= opens a session; a carried-over one shows a bar linking to
  where the conversation went on instead of the composer.
- The thread can open the previous session above the current one (shown
  only, never in the prompt), and replies get search_past_sessions and
  read_past_session.
- Sessions are named from their opening messages, not their latest, and
  a carried summary is labelled as the earlier session's.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

src/bots-queue/process-bot-job.ts

@@ -226,8 +226,12 @@ export default async function processBotJob({
          * a model that can't answer now leaves the session for the next
          * reply to name.
          */
-        if (job.kind == "reply" && completion.message && job.session_id) {
-            const session_id = Number(job.session_id);
+        if (job.kind == "reply" && completion.message?.session_id) {
+            /**
+             * The message's session, not the job's as it was claimed: a
+             * reply that moved the conversation on answered in the new one.
+             */
+            const session_id = Number(completion.message.session_id);
 
             /**
              * No job signal: the job is already complete, so its heartbeat