When I use the <details> element in a Content gadget, the <summary> tag is discarded and the word "Details" is display. See screenshot. (Yes, I had to edit the HTML in the Content gadget.)
If I use the custom HTML gadget, the <details> and <summary> elements are displayed as expected.
Here's a sample block of code:
<details >
<summary>Show/Hide me</summary>
<p>Quid me vexeri</p>
</details>

<details >
<summary>Even more great stuff</summary>
<p>So say we all</p>
</details>
</p>