Searching and version switching in the docs does not work

[AlexanderWells-diamond]

Expected Behavior

Using the "Search" bar in the documentation should allow me to search for keywords.

Using the "Choose version" drop-down should allow me to select from all published versions of the documentation.

Current Behavior

The "Search" bar does not work; nothing happens when I click on it. Not even a console error message.

The "Choose version" drop-down does not present a list of versions, it appears to render an empty drop-down.

Context

The broke "Search" is probably the same issue as described in bluesky/bluesky#1666 . I noticed it when doing the work for bluesky/bluesky#1706 and observed that changing the theme did not fix the "Search" bar.