Show a newly created bot in the rail at once

The rail was built from page props and only knew bots it already had, so a
bot the coordinator created did not appear until a reload.

create_bot and add_bot_to_workspace now push server:bot-created
(BotCreatedData) to everyone who sees the bot: its rail row, the
workspaces it is in, and whether it belongs in that user's own chat list.
useLiveBots inserts it, after the pinned coordinator outside a workspace
and only when the open workspace is one it joined. liveRelay pushes created
bots too, so a bot added by another process still shows.

src/live-relay/index.ts

@@ -3,6 +3,7 @@ import { AppData } from "@/src/data/app-data";
 import { logError } from "@/src/functions/backend/logger";
 import grabConnectedUserIds from "@/src/websocket/(functions)/grab-connected-user-ids";
 import relayChangedBots from "./relay-changed-bots";
+import relayCreatedBots from "./relay-created-bots";
 import relayNewBotMessages from "./relay-new-bot-messages";
 import relayNewJobUpdates from "./relay-new-job-updates";
 import type { LiveRelayCursor } from "./types";
@@ -50,7 +51,10 @@ export default async function liveRelay() {
              * Overlap one interval, so a change written in the same
              * millisecond as the last look isn't missed.
              */
-            await relayChangedBots({ since: cursor.bots_at - AppData.LiveRelayPollMs, users });
+            const bots_since = cursor.bots_at - AppData.LiveRelayPollMs;
+
+            await relayCreatedBots({ since: bots_since, users });
+            await relayChangedBots({ since: bots_since, users });
             cursor.bots_at = now;
         } catch (error) {
             await logError({ title: `Live relay failed`, error }).catch(() => {});