I love the idea ! Is there also a way to make sure you cannot remove these types of extensions ? Something open source and not sketchy that makes it possible to either set a password (that you'll not save) or be removed only if you reinstall the browser. Something to this liking ?
I don't think any browser vendor would expose an API to allow this.
I think the best you could manage is a system administrative profile that forces the browser to install the extension
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You could write your own OS software that polls your browser for installed extensions and then nukes your internet connection through the host file if you disable the extension. Cold Turkey kinda does this by automatically closing your browser during a blocked session if you disable their extension.
The challenge is that there's always a workaround. The added friction might be enough to fulfil your need though.