HTML Code

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="utf-8">
  <title>scoped text inputs</title>
  <style>
    body { font-family: sans-serif; padding: 16px; }
    form { margin-bottom: 16px; padding: 12px; border: 1px solid #e2e8f0; }
    input { display: block; margin: 6px 0; }
  </style>
</head>
<body>
  <form id="searchForm">
    <input type="text" placeholder="Old placeholder">
  </form>
  <form id="loginForm">
    <input type="text" placeholder="Username">
  </form>
  <script src="https://code.jquery.com/jquery-3.7.1.min.js"></script>
  <script>
    $("#searchForm input:text").attr("placeholder", "Search…");
  </script>
</body>
</html>

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Scoped #searchForm input:text (Try It)