I am using Ubuntu 18.04, but I think this problem is common in all Linux distros.
The search box (or the search "entry" in GTK's term) can't input any languages that need Input Method Support. This covers most non-latin languages. It's a lot.
I can provide two links with the technical details that may help you implement such a features. Though they are for GTK+2, but can apply to GTK+3 easily.