Without JavaScript, How Can I Append Something on to the SRC URL of an Image in wp_content() in WordPress?

Question

So I've discovered a scriptless way to detect webp support for images. It's fairly simple:

<?php if( strpos( $_SERVER['HTTP_ACCEPT'], 'image/webp' ) !== false ) { echo '.webp'; } ?>

Easy enough since most programs will convert the image to webp and just append ".webp" after the current extension. It's a great way to serve webp images without the use of plugins or scripts. In case anyone's curious, this is how that's used:

<img src="image.jpg<?php if( strpos( $_SERVER['HTTP_ACCEPT'], 'image/webp' ) !== false ) { echo '.webp'; } ?>" alt="">

Serverside webp detection rather than client site. OK. So my question is this: how do I do this with images placed into the content editor of WordPress? My template simply has this obviously to display that content:

<?php the_content(); ?>

Is there some way, via functions.php or wp-config.php, to use my snippet of code to append all images in the_content()? Plugins can do it with javascript, sure. But I want it to be done without the use of scripts. Just some simple php to say "for every instance of an image in wp_content, if webp is supported, append .webp onto that URL".

Can this be done? Thank you ahead of time!