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/functions/backend/db/bots/is-bot-in-own-chat.ts

@@ -0,0 +1,24 @@
+import BunSQLite from "@moduletrace/bun-sqlite";
+import chatBotsSql from "@/src/utils/crew-access/chat-bots-sql";
+import grabCrewRole from "../access/grab-crew-role";
+
+type Params = {
+    bot_id: number | string;
+    user_id: number | string;
+};
+
+/**
+ * Whether a bot belongs in a user's own chat list (`chatBotsSql`), as
+ * opposed to only a workspace they're in. Used to tell a client which
+ * rail a newly created bot shows up in.
+ */
+export default async function isBotInOwnChat({ bot_id, user_id }: Params) {
+    const access = chatBotsSql({ role: await grabCrewRole({ user_id }), user_id });
+
+    const res = await BunSQLite.sql<{ present: number }>({
+        sql: `SELECT 1 AS present FROM bots b WHERE b.id = ? AND ${access.sql} LIMIT 1`,
+        values: [bot_id, ...access.values],
+    });
+
+    return Boolean(res.payload?.[0]?.present);
+}