The search box and its buttons are in front of the leaflet map (otherwise they would be invisible), and anything the leaflet map contains. It's unlikely it's possible make the popups be in front, unless we use JS to put the search box inside the map (e.g. make it something like a leaflet control).
Even if we somehow did put the search box inside the map, it might be tricky. The popus are behind even the leaflet controls.
Closing since it's too trouble for what it's worth.
This is hard.
The search box and its buttons are in front of the leaflet map (otherwise they would be invisible), and anything the leaflet map contains. It's unlikely it's possible make the popups be in front, unless we use JS to put the search box inside the map (e.g. make it something like a leaflet control).
Even if we somehow did put the search box inside the map, it might be tricky. The popus are behind even the leaflet controls.
Closing since it's too trouble for what it's worth.