The net result of what this site is doing seems to result in one of two effects when I open the sidebar, randomly:

1) the sidebar covers the content, while the content has blank space to the right, or

2) the content moves off the right edge of the screen, leaving a large blank space to its left.

Both of these are wrong. If I have a sidebar open, the site is now narrower, stop trying to be clever.

My immediate reaction to this is why is the browser giving the site this information, and could we stop.

Agreed, both outcomes are bugs and neither is intended. The idea is simply that, content the site author intended to be horizontally centered stays literally centered on my screen when browser UI changes the viewport.