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/bots/insert-bot-message.ts

@@ -28,6 +28,11 @@ type Params = {
      * message in later turns (`botMessagesToHarness`).
      */
     tool_log?: HarnessToolUse[];
+    /**
+     * Opens a session the conversation moved into
+     * (`carryOverBotSession`): the session it carries on from.
+     */
+    carried_from_session_id?: number;
 };
 
 /**
@@ -43,6 +48,7 @@ export default async function insertBotMessage({
     interim,
     media_ids = [],
     tool_log,
+    carried_from_session_id,
 }: Params): Promise<BUN_SQLITE_COBBLE_BOT_MESSAGES> {
     const now = Date.now();
     const needs_you_flag = needs_you ? 1 : 0;
@@ -64,6 +70,7 @@ export default async function insertBotMessage({
                 needs_you: needs_you_flag,
                 interim: interim_flag,
                 tool_log: tool_log_json,
+                carried_from_session_id,
             },
         ],
     });
@@ -96,6 +103,7 @@ export default async function insertBotMessage({
         needs_you: needs_you_flag,
         interim: interim_flag,
         tool_log: tool_log_json,
+        carried_from_session_id,
         created_at: now,
         updated_at: now,
     };