There are significant challenges with trying to "restart" content scripts on a page at the platform level. Developers are better suited to make decisions about how to react to extension update events and (re)inject content scripts into pages than the browser, as we can't remove injected scripts and can't predict the side effects script injection will have.
That said, it should be possible to create an opinionated library/framework that uses the current capabilities of the extension platform to implement something like this.