Selenium C#中无法访问iframe内嵌PDF元素的问题求助

嗨，各位大佬！我最近在做Selenium自动化的时候，遇到了iframe内嵌PDF查看器的元素定位问题，卡了好一阵子，想请教下大家怎么解决。

首先跟大家说下页面的结构：
初始加载时，页面里是用来承载PDF的iframe，结构如下：

<div>
<iframe src="link.pdf" width="100%" height="500"> 
#document <!DOCTYPE html>
<html>
<head></head>
<body style="height: 100%; width: 100%; overflow: hidden; margin:0px; background-color: rgb(82, 86, 89);"><embed name="123333" style="position:absolute; left: 0; top: 0;" width="100%" height="100%" src="about:blank" type="application/pdf" internalid="1234"></body></html> 
</iframe>
</div>

当PDF加载完成后，通过开发者工具可以看到实际的DOM变成了带shadow DOM的PDF查看器结构：

<body>
<pdf-viewer id="viewer"></pdf-viewer>
> #shadow-root(open)
<viewer-toolbar id="toolbar">
> #shadow-root(open)
<div id="toolbar">
  <div id="start">
    <cr-icon-button id="sidenavToggle" title="Menu" aria-label="Menu" iron-icon="cr20:menu" aria-expanded="true" role="button" tabindex="0" aria-disabled="false">
    </cr-icon-button>
    <span id="title"><!--?lit$02748104126$-->D5F1C5BE75754D2065258671002817C2_GAQC_Alert_No._421.pdf</span>
  </div>
  <div id="center">
    <viewer-page-selector style="--page-length-digits: 1;">
    </viewer-page-selector>
    <span class="vertical-separator"></span>
    <span id="zoom-controls">
      <cr-icon-button title="Zoom out" aria-label="Zoom out" iron-icon="pdf:remove" role="button" tabindex="0" aria-disabled="false">
      </cr-icon-button>
      <input type="text" value="100%" aria-label="Zoom level">
      
      <cr-icon-button title="Zoom in" aria-label="Zoom in" iron-icon="pdf:add" role="button" tabindex="0" aria-disabled="false">
      </cr-icon-button>
    </span>
    <span class="vertical-separator"></span>
    <cr-icon-button id="fit" title="Fit to page" aria-label="Fit to page" iron-icon="pdf:fit-to-height" role="button" tabindex="0" aria-disabled="false">
    </cr-icon-button>
    <cr-icon-button id="rotate" suppress-rtl-flip="" aria-label="Rotate counterclockwise" title="Rotate counterclockwise" iron-icon="pdf:rotate-left" role="button" tabindex="0" aria-disabled="false">
    </cr-icon-button>

    <!--?lit$02748104126$-->

  </div>
  <div id="end">
  
    <viewer-download-controls id="downloads">
    </viewer-download-controls>
    <cr-icon-button id="print" title="Print" aria-label="Print" iron-icon="cr:print" role="button" tabindex="0" aria-disabled="false">
    </cr-icon-button>
    <cr-icon-button id="more" title="More actions" aria-label="More actions" iron-icon="cr:more-vert" role="button" tabindex="0" aria-disabled="false"></cr-icon-button>
  </div>
</div>
</viewer-toolbar>
</body>

我写的C#代码尝试定位并点击下载按钮，代码如下：

frameElement = WebElementFinder.GetElement(Driver, XPATHOFFrame);
Driver.SwitchTo().Frame(frameElement);

IWebElement elementInsideIframe = Driver.FindElement(By.TagName("embed"));
IWebElement shadowHost1 = Driver.FindElement(By.Id("viewer"));
ISearchContext shadowRoot1 = shadowHost1.GetShadowRoot();
IWebElement shadowHost2 = shadowRoot1.FindElement(By.Id("toolbar"));
ISearchContext shadowRoot2 = shadowHost2.GetShadowRoot();
IWebElement shadowHost3 = Driver.FindElement(By.Id("downloads"));
ISearchContext shadowRoot3 = shadowHost3.GetShadowRoot();
IWebElement shadowHost4 = Driver.FindElement(By.Id("download"));
ISearchContext shadowRoot4 = shadowHost3.GetShadowRoot();
shadowRoot4.FindElement(By.Id("icon")).Click();

但运行时抛出了异常：

"no such element: Unable to locate element: {"method":"css selector","selector":"#viewer"

想问问大家，这个问题出在哪？怎么才能正确定位到PDF查看器里的下载按钮呢？麻烦大家帮忙指点一下，谢谢啦！

备注：内容来源于stack exchange，提问作者ayushi