Bug: 'Pick a month' does not synchronise from Archive list

There are two ways of selecting the month:

The Archive: buttons in the left hand column, or the 'Pick a month' drop-down, which is used when the display is too narrow for the archive list.

When switching from narrow to wide, the currently selected month in the drop-down is correctly propagated to the Archive: buttons.

However when the screen is narrowed, the correspond entry in the drop-down is not selected (it looks like it selects whatever was last chosen).

This is misleading as it does not match the display, and causes a problem if the user actually wants to view the entry in the drop-down. Since the entry is already selected, opening and closing the drop-down does not work. The user has to select a different entry first.

Trace the Archive buttons and the “Pick a month” drop-down to find where their selected month is synchronized during responsive layout changes. Reproduce narrowing the screen from wide to narrow, then verify that the drop-down selection matches the displayed archive month and can be opened without first choosing another entry.

Written by the indexing model from the issue text.