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/app-settings/grab-bot-session-max-messages.ts

@@ -0,0 +1,31 @@
+import { AppData } from "@/src/data/app-data";
+import { BotSessionMaxMessagesSettingKey } from "@/src/dict/bot-dict";
+import type { SessionLengthOverview } from "@/src/types";
+import readStepLimit from "@/src/utils/read-step-limit";
+import grabAppSetting from "./grab-app-setting";
+
+/**
+ * How many messages a session takes before the user's next message starts
+ * a new one: the install's own number (`bot_session_max_messages`,
+ * Settings > General), else `AppData.BotSessionMaxMessages`.
+ */
+export async function grabBotSessionMaxMessages() {
+    return readStepLimit({
+        saved: await grabAppSetting({ key: BotSessionMaxMessagesSettingKey }),
+        fallback: AppData.BotSessionMaxMessages,
+        max: AppData.BotSessionMaxMessagesMax,
+    });
+}
+
+/**
+ * The number with its default and ceiling, for the settings page.
+ */
+export default async function grabSessionLengthOverview() {
+    const overview: SessionLengthOverview = {
+        max_messages: await grabBotSessionMaxMessages(),
+        default_messages: AppData.BotSessionMaxMessages,
+        max: AppData.BotSessionMaxMessagesMax,
+    };
+
+    return overview;
+}