The ArcGIS Pro search index does not return non-enterprise geodatabase results when an enterprise geodatabase connection exists in the project and the OS regional language is set to Russian.
I can't reproduce this problem with Pro 2.3 with the information provided. The OS is set to Russian, and no language pack is installed. The new project contains only the default geodatabase, the default toolbox, and the map and the new enterprise geodatabase connection that were added following the provided steps. Every time, I get the Map returned in the search results. More information will be needed to define a reproducible case if the customer can still reproduce the problem with Pro 2.3.