fix(web): wire Refresh Groups button to syncGroupsAction with live SSE refresh

The button was a placeholder that submitted to a no-op server action,
so clicking did nothing. Replace with a small client component that:

  1. Calls syncGroupsAction(accountId) to pgNotify the bot.
  2. Listens for the bot's groups.synced event over SSE and
     router.refresh()es when it arrives so the new rows appear without
     a manual reload.
  3. Disables the button + shows a Syncing… label while the sync is
     in flight, with a 15s safety timeout if the bot or SSE channel
     drops so the spinner doesn't strand.

Drop the in-place <form action={async() => 'use server'}> placeholder.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/web/src/app/accounts/[id]/groups/page.tsx

@@ -4,7 +4,6 @@ import {
   ArrowLeftIcon,
   SearchIcon,
   UsersIcon,
-  RefreshCwIcon,
   Users2Icon,
 } from "lucide-react";
 import { Button } from "@/components/ui/button";
@@ -16,6 +15,7 @@ import {
 } from "@/components/ui/card";
 import { getSeededOperator } from "@/lib/operator";
 import { listGroupsForAccount } from "@/lib/queries";
+import { RefreshGroupsClient } from "./refresh-groups-client";
 
 interface Props {
   params: Promise<{ id: string }>;
@@ -57,13 +57,7 @@ export default async function GroupsListPage({ params, searchParams }: Props) {
           </Badge>
         </div>
 
-        {/* Refresh button — no-op placeholder, wired in Task 17 */}
-        <form action={async () => { "use server"; /* wired in Task 17 */ }}>
-          <Button type="submit" variant="outline" size="sm" className="shrink-0">
-            <RefreshCwIcon />
-            Refresh Groups
-          </Button>
-        </form>
+        <RefreshGroupsClient accountId={account.id} />
       </div>
 
       {/* Search */}

apps/web/src/app/accounts/[id]/groups/refresh-groups-client.tsx

@@ -0,0 +1,68 @@
+"use client";
+
+import { useState, useTransition } from "react";
+import { useRouter } from "next/navigation";
+import { Loader2Icon, RefreshCwIcon } from "lucide-react";
+import { Button } from "@/components/ui/button";
+import { useEvents } from "@/hooks/use-events";
+import { syncGroupsAction } from "@/actions/accounts";
+
+interface RefreshGroupsClientProps {
+  accountId: string;
+}
+
+/**
+ * Two-stage refresh button:
+ *  1. Click → server action pgNotifies the bot to start a sync.
+ *  2. Bot finishes → emits `groups.synced` over SSE → router.refresh()
+ *     re-fetches the page so the new rows appear without the operator
+ *     having to reload manually.
+ *
+ * The button stays in its "syncing" state until either the
+ * `groups.synced` event arrives for this account or 15 s pass (so a
+ * disconnected bot doesn't strand the spinner forever).
+ */
+export function RefreshGroupsClient({ accountId }: RefreshGroupsClientProps) {
+  const router = useRouter();
+  const [pending, start] = useTransition();
+  const [waiting, setWaiting] = useState(false);
+
+  useEvents({
+    "groups.synced": (data) => {
+      if (data.accountId !== accountId) return;
+      setWaiting(false);
+      router.refresh();
+    },
+  });
+
+  function trigger() {
+    start(async () => {
+      const fd = new FormData();
+      fd.append("accountId", accountId);
+      await syncGroupsAction(fd);
+      setWaiting(true);
+      // Belt-and-braces: if the bot is unreachable or the SSE channel
+      // drops, drop the spinner after 15 s instead of leaving it stuck.
+      window.setTimeout(() => setWaiting(false), 15_000);
+    });
+  }
+
+  const busy = pending || waiting;
+  return (
+    <Button
+      type="button"
+      variant="outline"
+      size="sm"
+      className="shrink-0"
+      disabled={busy}
+      onClick={trigger}
+    >
+      {busy ? (
+        <Loader2Icon className="size-4 animate-spin" />
+      ) : (
+        <RefreshCwIcon className="size-4" />
+      )}
+      {busy ? "Syncing…" : "Refresh Groups"}
+    </Button>
+  );
+}