You should be able to toggle collapsible sections - if you can't, you're likely in the Rich Text Editor instead of the Markdown Editor. Make sure you're on the left/red side of the toggle in the image below, which swaps between the two - then use the blue button to swap between the editor and the webview, which is where you'll be able to view and toggle the collapsible sections.
You may also be interested in my collapsible block plugin, which allows for the creation of these blocks without having to type out the HTML, and with a few other features. So instead of:
<details><summary>Title</summary>Body</details>
you'd write
:{Title
Body
}:
Note that my plugin won't work in the Rich Text Editor either - most won't. I just stick with the Markdown editor 100% of the time, and I think that's pretty common.