Thank you for reporting a bug to Unity.
The root cause of the issue is that only filenames support infix search. The Template Browser searches by filenames and other indexed search words, like the Template's Name. These are handled and treated separately, but when named the same gives the impression that the infix searches are supported for some assets and not others.
I'm passing this along as a feature request to the search team to enable or allow infix searching for select indices.