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/session-name-transcript.ts

@@ -0,0 +1,21 @@
+import type { SessionOpeningMessage } from "@/src/functions/backend/db/bot-sessions/grab-session-opening";
+
+type Params = {
+    messages: SessionOpeningMessage[];
+};
+
+/**
+ * A session's opening as the naming turn reads it. The summary that opens
+ * a session the bot moved the conversation into is marked as the earlier
+ * session's, so the title says what this one carries on with rather than
+ * echoing everything the summary recaps.
+ */
+export default function sessionNameTranscript({ messages }: Params) {
+    return messages
+        .map((message) =>
+            message.carried_from_session_id
+                ? `(Summary of the earlier session this one carries on from)\n${message.text || ""}`
+                : `${message.author == "user" ? "User" : "You"}: ${message.text || "(files only)"}`,
+        )
+        .join("\n\n");
+}