So I was able to achieve what I wanted, albeit in a bit of a roundabout way. I'll share my solution here in case anyone stumbles across this post looking to do something similar.

Rather than adding an event listener to some unset event (that doesn't exist) on the object returned by wp.media.featuredImage.frame(), I instead added my own onclick event listener to the #remove-post-thumbnail link element. This feels a little hacky to me, since its not directly tied to the unset of a featured image, however since there's no prompt to verify removal, the user interaction is fairly seemless.

There is a caveat with this solution, however - there is already an onclick event bound to that link. Originally I tried capturing that default onclick event and then calling it from within my own event that overrides it, like so:

var ogCallback = document.getElementById('remove-post-thumbnail').onclick;
document.getElementById('remove-post-thumbnail').onclick = function(e) {
    // My code - do some things
    // ...
    ogCallback(e);
}

But this made WordPress a little buggy when removing the featured image, likely due to some JavaScript scoping that I wasn't taking into account. Because I'm also leveraging jQuery (this is a judgment-free zone, right?) I was able to use jQuery's event binding system instead, and avoid overriding the default behaviour, allowing my custom code to run in tandem with WordPress' featured image removal logic:

$(document).on('click', '#remove-post-thumbnail', function(){
    // Do stuff. Don't let your dreams be dreams
});

So I was able to achieve what I wanted, albeit in a bit of a roundabout way. I'll share my solution here in case anyone stumbles across this post looking to do something similar.

Rather than adding an event listener to some unset event (that doesn't exist) on the object returned by wp.media.featuredImage.frame(), I instead added my own onclick event listener to the #remove-post-thumbnail link element. This feels a little hacky to me, since its not directly tied to the unset of a featured image, however since there's no prompt to verify removal, the user interaction is fairly seemless.

There is a caveat with this solution, however - there is already an onclick event bound to that link, so you need to avoid overriding that, or else you won't be able to actually remove the featured image. Originally I tried capturing that default onclick event and then calling it from within my own event that overrides it, like so:

DO NOT DO THIS

var ogCallback = document.getElementById('remove-post-thumbnail').onclick;
document.getElementById('remove-post-thumbnail').onclick = function(e) {
    // My code - do some things
    // ...
    ogCallback(e);
}

But this made WordPress a little buggy when removing the featured image, likely due to some JavaScript scoping that I wasn't taking into account. Because I'm also leveraging jQuery (this is a judgment-free zone, right?) I was able to use jQuery's event binding system instead, and avoid overriding the default behaviour, allowing my custom code to run in tandem with WordPress' featured image removal logic:

DO THIS

$(document).on('click', '#remove-post-thumbnail', function(){
    // Do stuff. Don't let your dreams be dreams
});