Name sessions with the model and keep the rail list live

Sessions no longer take their title from the first message: once the first exchange is sent, the text model writes the title and summary, which the rail and sessions list show. The summary records how many messages it covers so a stale one is rewritten before it is carried into the next session.

The sessions hook now reloads on live message and session events, so a session started by the first message, a rollover or another tab appears without a reload. New sessions are pushed as server:bot-session, both from the process that changed them and through the live relay.

src/functions/backend/db/bot-sessions/start-bot-session.ts

@@ -14,8 +14,9 @@ type Params = {
 
 /**
  * Closes the conversation's active session and starts the next one, which
- * carries on from it (its summary is written when the next reply runs).
- * An active session with no messages yet is kept as it is.
+ * carries on from it (its summary goes into the next reply's prompt,
+ * rewritten first when it covers fewer messages than the session ended
+ * with). An active session with no messages yet is kept as it is.
  */
 export default async function startBotSession({
     user_id,

src/functions/backend/db/bots/insert-user-message.ts

@@ -24,8 +24,9 @@ type Params = {
 
 /**
  * Appends a user message (and its files) to a session and bumps its
- * activity. The first one titles the session. Callers must check the bot
- * and session belong to the session user first.
+ * activity. The session is named later, from its first exchange with the
+ * bot (`nameBotSession`). Callers must check the bot and session belong to
+ * the session user first.
  */
 export default async function insertUserMessage({
     bot_id,
@@ -66,13 +67,9 @@ export default async function insertUserMessage({
         });
     }
 
-    const title = (text || media[0]?.title || "").replace(/\s+/g, " ").trim().slice(0, 80);
-
     await BunSQLite.sql({
-        sql: `UPDATE bot_sessions SET last_activity_at = ?,
-            title = CASE WHEN COALESCE(title, '') = '' THEN ? ELSE title END
-            WHERE id = ?`,
-        values: [now, title, session_id],
+        sql: `UPDATE bot_sessions SET last_activity_at = ? WHERE id = ?`,
+        values: [now, session_id],
     });
 
     return {