Two websites, same server. One site has broken images on the Settings page, and the other one does not.

For example:
On the site without broken images, the URL to an image is:
<img draggable="false" role="img" class="emoji" alt="☂️" src="https://s.w.org/images/core/emoji/14.0.0/svg/2602.svg">

On the site with broken images, the URL to an image is:
<img draggable="false" role="img" class="emoji" alt="☔" src="https://twemoji.maxcdn.com/v/14.0.2/2614.svg">

Clearing the cache and browser, purging the cache plugin, and deleting and installing the plugin again didn't solve it.