问题似乎是因为用于包含jquery代码的语法是立即调用的函数表达式（iife），而不是jquery document.ready处理程序。这意味着您的代码是在加载dom之前运行的，因此您试图绑定事件处理程序的元素还不存在。
要解决此问题，请使用标准jquery document.ready事件处理程序：

jQuery($ => {
  // sticky footer form class toggle on click
  $(".nb-form .form-header").on("click", () => {
    $(".nb-form").toggleClass("open");
  });
});

/* Note this CSS is only for demo purposes and isn't relevant to the issue */
img { width: 50px; }
.nb-form .form-content { display: none; }
.nb-form.open .form-content { display: block; }

<script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.3.1/jquery.min.js"></script>
<div class="nb-form">
  <div class="form-header">
    <p class="title">Request a Quote</p>
    <img src="https://soldaf.ca/wp-content/uploads/2020/11/Andrew-headshot-e1606168346405.jpg" alt="Andrew Foster" class="user-icon" />
  </div>

  <div class="form-content">
    <p class="message">Send us a message or give us a call at <span class="d-inline-block">(403) 915-6195.</span></p>
    <?php echo do_shortcode( '[[contact-form-7 id="4545" title="Contact form 1"]]' ); ?>
  </div>
</div>

请尝试使用此代码

<div class="nb-form">
    <div class="form-header">
        <p class="title">Request a Quote</p>
        <img src="https://soldaf.ca/wp-content/uploads/2020/11/Andrew-headshot-e1606168346405.jpg" alt="Andrew Foster" class="user-icon">
    </div>    

    <div class="form-content">
        <p class="message">Send us a message or give us a call at <span class="d-inline-block">(403) 915-6195.</span></p>   
        <?php echo do_shortcode( '[[contact-form-7 id="4545" title="Contact form 1"]]' ); ?>
    </div>
</div>

jquery

$(".nb-form .form-header").on("click", function () {
    $(".nb-form .form-content").toggleClass("open");
    // or else you can use toggle method
    $(".nb-form .form-content").toggle()
});