Name sessions opened by handed-off work, and hide empty ones from activity

A session the coordinator's delegation, a routine or a hook opened has
no user message and no reply, so it was never named and showed as
"Untitled conversation". Tasks now name their session too, and a session
with no user message is named from the bot's own messages. Until a
session is named, Latest activity shows what it opened with, and
sessions with no messages are left out of it.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

src/bots-queue/session-ready-to-name.ts

@@ -0,0 +1,28 @@
+import type { SessionOpeningMessage } from "@/src/functions/backend/db/bot-sessions/grab-session-opening";
+
+type Params = {
+    messages: SessionOpeningMessage[];
+};
+
+/**
+ * Whether a session's opening says enough to name it: the bot has said
+ * something of its own (a carried summary doesn't count), and, when the
+ * user wrote, after the user's first message. A session with no user
+ * message at all is work handed to the bot (the coordinator's delegations,
+ * routines, hooks), named from the bot's own messages.
+ */
+export default function sessionReadyToName({ messages }: Params) {
+    const has_bot_message = messages.some(
+        (message) => message.author == "bot" && !message.carried_from_session_id,
+    );
+
+    if (!has_bot_message) return false;
+
+    const first_user = messages.findIndex((message) => message.author == "user");
+
+    if (first_user < 0) return true;
+
+    return messages
+        .slice(first_user + 1)
+        .some((message) => message.author == "bot" && !message.carried_from_session_id);
+}