This new design is 164px wider due to the new left sidebar as far as I've seen from the Teams beta. Assuming that not everyone has SE open fullscreen in wide monitors, the site should still be as useable as now if the screen is only as wide as the current design. Wide high-resolution screens are pretty common now, but they're also really useful to put things side-by-side, so it doesn't mean that space is available.
The right sidebar is more important in some contexts than the left one, but you're hiding it first in the responsive design. Monica Cellio already mentioned aspects of this, but I'll add a bit more on this.
The left sidebar contains the links to the homepage, the questions list, tags, users and jobs (ignoring Teams for now, as most users won't have that). That some really important links like the homepage and questions, and some that are likely used much less like tags and users. It feels like a lot of wasted space for the few truly important functions there.
The right sidebar is a mix of extremely useful items like favorite tags, and expendable stuff like Hot Network Questions. It also contains e.g. the "How to ask" section on the Ask Question page, and likely some other useful stuff on other pages I can't think of right now. The favorite tags element is probably the navigation tool I use the most often on sites where I have multiple favorites defined. On a few sites, the right column contains a professional-advice disclaimer that is very important to the members of those communities.
In your new design, the sidebar is hidden early, and in this case it really shouldn't contain any elements that are very important. Currently you have two sidebars which both contain important elements, and that means important stuff gets hidden the moment your window is narrower than the maximum width of the new design.
If you decide to stay mostly with the design as proposed, I think the non-fluff elements of the right sidebar should either be moved, or have alternative forms once the design gets too narrow for the sidebar. Otherwise the site becomes far less usable on narrow windows.