Here's what I'd expect it to behave like, though I know it isn't currently the case
The control centers setting should be named and work as the "default" setting. Such as 'default search region'.
The filter when searching should always be the default unless changed for a specific search.
Say I search "pizza" and my default is UK, I'll get UK in the filter, I could then quick ly toggle the filter to Italy which will change the results to Italian results for this search/session only. After which the filter will return to what is the default set in the control center.