feat(admin): 'List on request page' toggle on project page

Phase 9a Task 5. Single switch, owner-only via the Server Action
wired in Task 4. Saves immediately on click; reverts on error so
a transient PB failure can't leave the UI lying. Default off, per
the Phase 9 spec §4.5.

src/app/admin/projects/[projectId]/page.tsx

@@ -6,6 +6,7 @@ import { IngestPanel } from "@/components/admin/ingest-panel";
 import { SummaryPanel } from "@/components/admin/summary-panel";
 import { IntakeLinksPanel } from "@/components/admin/intake-links-panel";
 import { BackgroundMdEditor } from "@/components/admin/background-md-editor";
+import { ShowInIntakeToggle } from "@/components/admin/show-in-intake-toggle";
 import { getAdminPb } from "@/lib/pb/admin";
 import { summaryStatus } from "@/lib/ai/summarise";
 import type { IntakeLinkRecord, ProjectRecord } from "@/lib/pb/types";
@@ -65,6 +66,10 @@ export default async function ProjectAdminPage({
           />
           <SummaryPanel projectId={project.id} status={summary} />
           <IntakeLinksPanel projectId={project.id} links={links} />
+          <ShowInIntakeToggle
+            projectId={project.id}
+            initial={Boolean(project.show_in_intake)}
+          />
           <BackgroundMdEditor
             projectId={project.id}
             initial={project.background_md}

src/components/admin/show-in-intake-toggle.tsx

@@ -0,0 +1,87 @@
+"use client";
+
+import { useState, useTransition } from "react";
+
+import { setProjectShowInIntakeAction } from "@/app/actions/project-show-in-intake";
+
+/**
+ * The "List on request page" toggle on the project admin page.
+ *
+ * Default off. When on, the project appears in the public intake picker
+ * under any client link that targets this project's client. The flag is
+ * the leak-prevention boundary — see the Phase 9 spec §3.
+ *
+ * Two clicks to flip; no confirm dialog because the flip is reversible
+ * from the same surface.
+ */
+export function ShowInIntakeToggle({
+  projectId,
+  initial,
+}: {
+  projectId: string;
+  initial: boolean;
+}) {
+  const [value, setValue] = useState(initial);
+  const [pending, startTransition] = useTransition();
+  const [saved, setSaved] = useState<boolean>(false);
+  const [error, setError] = useState<string | null>(null);
+
+  function flip() {
+    const next = !value;
+    setValue(next);
+    setSaved(false);
+    setError(null);
+    startTransition(async () => {
+      try {
+        await setProjectShowInIntakeAction({ projectId, show: next });
+        setSaved(true);
+      } catch (e) {
+        setError(e instanceof Error ? e.message : "Could not save");
+        setValue(!next); // revert
+      }
+    });
+  }
+
+  return (
+    <section className="flex items-center justify-between gap-3 rounded-[var(--radius-tile)] border border-border-subtle p-4">
+      <div>
+        <h2 className="text-sm font-semibold text-text-primary">
+          List on request page
+        </h2>
+        <p className="mt-0.5 text-xs text-text-muted">
+          Show this project in the public request page's project picker.
+          Off by default.
+        </p>
+      </div>
+      <div className="flex items-center gap-2">
+        <button
+          type="button"
+          role="switch"
+          aria-checked={value}
+          disabled={pending}
+          onClick={flip}
+          className={
+            "inline-flex h-6 w-11 items-center rounded-full transition-colors disabled:opacity-50 " +
+            (value ? "bg-brand" : "bg-border-subtle")
+          }
+        >
+          <span
+            className={
+              "inline-block h-5 w-5 transform rounded-full bg-white shadow transition-transform " +
+              (value ? "translate-x-5" : "translate-x-0.5")
+            }
+          />
+        </button>
+        {pending && <span className="text-xs text-text-muted">Saving…</span>}
+        {error && (
+          <span role="alert" className="text-xs text-accent">
+            {error}
+          </span>
+        )}
+        {!pending && saved && (
+          <span className="text-xs text-text-muted">Saved.</span>
+        )}
+      </div>
+    </section>
+  );
+}