All I have to show for direct monetary damages is a drop in conversions if I’m using that site to sell or inform people about a product or a service.

If they’re changing the content of my website before showing it to viewers without my permission that also gets into copyright, tortious interference, possibly trademark, and maybe even CFAA causes.

I imagine this would be an opt-in service. Either the user uses a special browser that’s clearly marketed to do exactly this as opposed to the original content or the website operator opts in to having their content updated on the fly for users like this.