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/functions/backend/db/bot-sessions/grab-carried-to-session-id.ts

@@ -0,0 +1,22 @@
+import BunSQLite from "@moduletrace/bun-sqlite";
+
+type Params = {
+    session_id: number | string;
+    user_id: number | string;
+};
+
+/**
+ * The session a closed session of the user's was carried into
+ * (`carryOverBotSession`), or null when it wasn't carried over.
+ */
+export default async function grabCarriedToSessionId({ session_id, user_id }: Params): Promise<number | null> {
+    const carried = (
+        await BunSQLite.sql<{ session_id: number }>({
+            sql: `SELECT m.session_id FROM bot_messages m JOIN bot_sessions s ON s.id = m.session_id
+                WHERE m.carried_from_session_id = ? AND s.user_id = ? ORDER BY m.id DESC LIMIT 1`,
+            values: [session_id, user_id],
+        })
+    ).payload?.[0];
+
+    return carried?.session_id ? Number(carried.session_id) : null;
+}