Does anyone know if images can be converted at the server-level? We have hundreds of thousands of images - mostly in jpeg format. My question is: can the images (that are uploaded to our Amazon server) be converted there and then? The format I am interested in using would be something like Webp - so the conversion would be JPEG > WEBP
The answer to your question is "yes".
Assuming you have your own custom site with your own code written in PHP, you would use something like https://imagemagick.org or https://github.com/free-open-source/php-image-converter (I have no connection - found by doing a basic search).
There are many other options, you would need to do your own research to find out which suits your site.
Since you are posting on webmasters, I assume that your server is hosting your backend with some "web-based" language.
Since Nodejs seems the most popular, I suggest you to look at Sharp.
You can also use the Nodejs AWS SDK to make it in one script: documentation
As @Steve said, there is a lot of options here. You have to be more specific on your question.
If your AWS instance is just a storage node then you would need a processing server which can download the image, convert it, and upload it back to AWS.
If your AWS instance does more then you can use a backend programming language to make the conversions.
How are the images being uploaded exactly? If people are using FTP directly then you'll need to schedule a scan of your server to convert stuff to webp.
If the images are being uploaded through a front-end like WordPress then you need to program WP to convert the images before uploading them. Albeit, you will still have to figure out a solution for existing images.