Make scheduler logout clear session

apps/scheduler/components/AuthCard.tsx

@@ -1,6 +1,7 @@
 import Link from "next/link";
 
 import { AuthentikLoginButton } from "@scheduler/components/AuthentikLoginButton";
+import { AuthentikLogoutButton } from "@scheduler/components/AuthentikLogoutButton";
 import { safeSchedulerCallback } from "@scheduler/lib/scheduler/auth-links";
 
 type AuthCardProps = {
@@ -35,9 +36,7 @@ export function AuthCard({ mode, callbackUrl }: AuthCardProps) {
         {isLogin ? (
           <AuthentikLoginButton callbackUrl={safeCallbackUrl} />
         ) : (
-          <Link className="auth-primary" href="/auth/logout">
-            Sign out
-          </Link>
+          <AuthentikLogoutButton />
         )}
         {!isLogin && (
           <Link className="auth-secondary" href="/calendar">

apps/scheduler/components/AuthentikLogoutButton.tsx

@@ -0,0 +1,16 @@
+"use client";
+
+import { signOut } from "next-auth/react";
+
+export function AuthentikLogoutButton() {
+  return (
+    <button
+      className="auth-primary"
+      type="button"
+      onClick={() => {
+        void signOut({ callbackUrl: "/login" });
+      }}>
+      Sign out
+    </button>
+  );
+}