Entirely executing within the browser sandbox is one way to mitigate this. And that is the current scope of the official w3c proposal for this.

https://github.com/webmachinelearning/webmcp

I attempted to acknowledge the security implications and am not trying to push this as a product/service - this was just a proposal.

Despite it being a proposal, I added token based authentication to mitigate potential abuse by forcing users to intentionally authenticate with a website before it can be used.