You need to open a bug in order to make developers aware of this bug. We normally search on the bug tracker which bugs needs to be resolved.
As this an open source project there is no estimated time of resolution of a bug, so if you want to be fixed soon the best option is to report and contribute a patch for it.
I tested the search on the demo site and the search worked fine. I thought maybe the behavior was different using the client so I did a docker install and again, the search worked fine.
Something had to be wrong with my original install.
The reason the Search widget did not work for me when I did a manual install of Tryton is because Debian Buster uses PostgreSQL 11. When I updated to PostgreSQL 12 (which is the version used in the Docker install), the search worked.