I had a quick look at this. I saw how his search also has an add tiddler feature, So I though as a work around you could put the standard search into the left sidebar. So I created a tiddler containin
<<tag $:/tags/SideBarSegment>> so I could see if all I needed to do was tag the standard search tiddler $:/core/ui/SideBarSegments/search with $:/tags/SideBarSegment.
The first observation is I can’t even read the tag popup as it is truncated by the bottom of the tiddler.
What this tells me is the search is possibly not working because the tiddlers have a higher z-index than the tag drop down (as opposed to X width and Y height the Z is depth), and this is possibly also happening with the custom search in the theme.
So I did go to tag the standard search tiddler $:/core/ui/SideBarSegments/search with $:/tags/SideBarSegment and found it already was. I notices then the left side bar displays those items with the tag $:/tags/SideBar so I found the shadow tiddler $:/core/ui/SideBarSegments/search and tagged it with $:/tags/SideBar and we have the same problem.
We need either the theme author to look at this or the core dev team to tell us if there were any z-index changes in the 5.2.0 release.
I raised this here Were their any z-Index changes in the 5.2.0 core release?