Hi Lawrence,
Thanks for writing in! Alt text is not pulled from the media library itself, however you can set it through the image element in Cornerstone.
I have actually tested this on my end and I can confirm that the Alt information is displaying correctly on the browser, when we set it in the Cornerstone image element.


Upon further testing, I see that you’re using a caching plugin on your site. Please make sure to purge your server cache, also clear browser cache and test your issue again (https://www.wpbeginner.com/beginners-guide/how-to-clear-your-cache-in-wordpress/).
If you’re still having issues, you can try disabling your 3rd party plugins to see if you’re experiencing any plugin conflict. If the issue resolved, then you can enable your plugins one by one to see which plugin causing the issue.
Let us know how it goes.
Thanks!