Requested feature overview description.
When navigating the site, things like what dropdown selection for the search page or what set a post is being added to remain persistent across pages until changed. So why not with the dropdowns for tag category lists hen collapsing them?

Why would it be useful?
It would improve User Experience. Those who do not want to use it will not be effected as it will stay open.

What part(s) of the site page(s) are affected?
Post pages