It would be great to be able to search for many layers, tin, raster, table, etc. in many FGDB in the catalog.
Can you provide any additional details beyond a request for general Search, which is already possible?
Search project and portal items—ArcGIS Pro | ArcGIS Desktop
Not to nitpick with semantics, but I think semantics matter when asking Esri to implement new functionality. Geodatabases don't store layers, so are you asking them to start; or are you asking them about searching for data that is already able to be stored in a geodatabase?
Retrieving data ...