For interactive sites, if videos were limited to 480p on mobile and 720p on desktop unless manually changed, I imagine the carbon impact of data centers would drop considerably. For content viewed on TVs (where you usually sit quite a bit farther back than a monitor), such as Netflix or Hulu, I think they could set it to 480p by default and a lot of people would never bother to change it.

Unfortunately actually calculating the carbon footprint of a bloated web (compared to a lite version) would be very difficult. As you mention, a lot of that bloat is on the backend. New Reddit may transfer 6x more resources over the network than Old Reddit, but both of them have to process on the back-end what links should even be shown for a given user, so I doubt switching to Old Reddit would result in 6x fewer emissions. But even if it only resulted in 2x fewer emissions, that'd still be a considerable improvement. Part of the investigation would require seeing how much energy is used by the data centers processing what to send, versus how much energy is used by ISPs transferring that data across networks to the end-users.

In any case, if sites were more like Hacker News, Craigslist, and Wikipedia, versus New Reddit, Amazon, and most news sites, I feel confident that the carbon footprint of the Internet would go down notably. HN and Craigslist's designs are going to be hard sell for most businesses, but something like Wikipedia proves you can have an attractive design with low page sizes. And in the case for newspapers, it'd be nice if their web versions were more similar to their paper versions. That is tough with a free + ads model, but honestly I'm more likely to see an ad if the whole site is just text and there's a text ad in the middle of it (hopefully properly identified as such, though.)