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/pages/admin/bots/[bot_id]/(partials)/message-group-block.tsx

@@ -2,16 +2,31 @@ import type { BotWithLastMessage } from "@/src/types";
 import type { MessageGroup } from "../(utils)/group-messages";
 import UserMessageGroup from "./user-message-group";
 import BotMessageGroup from "./bot-message-group";
+import SessionDivider from "./session-divider";
 
 type Props = {
     bot: BotWithLastMessage;
     group: MessageGroup;
 };
 
+/**
+ * One author's group, under a divider when it starts a later session than
+ * the messages above it.
+ */
 export default function MessageGroupBlock({ bot, group }: Props) {
-    if (group.author === "user") {
-        return <UserMessageGroup bot={bot} group={group} />;
-    }
+    const block =
+        group.author === "user" ? (
+            <UserMessageGroup bot={bot} group={group} />
+        ) : (
+            <BotMessageGroup bot={bot} group={group} />
+        );
 
-    return <BotMessageGroup bot={bot} group={group} />;
+    if (!group.starts_session) return block;
+
+    return (
+        <>
+            <SessionDivider />
+            {block}
+        </>
+    );
 }