Thanks for your answer!
It looks like Twitter no longer adheres to the ratio in the desktop UI (it comes out to about ~2.0 in this case). By their own admission, it’s only used at the smallest width, so it should be seen as more of a lower limit of usability and not a ratio that is ideal for all browser window sizes.
My hunch on what’s really going on here is that, to establish visual hierarchy, the hierarchy is most clear when the secondary column is about half the width of the primary column (or gives that impression, at least). Humans in their perceptions probably overestimate the size of small objects and underestimate the side of large objects in relation to each other(need source). So perhaps the Golden Ratio is a manifestation of this cognitive bias and is the ratio where the first smaller area appears to be about half the size even though it’s more than half.
Twitter seems to be following the heuristic of about ~70 character line width for optimal readability. (I count 78 characters in the first visible tweet).