It would be nice if the quick search (the "thing" opened via `Ctrl + Alt + O`) would match the search term against the full file path. I would find that very useful because often one has multiple files with the same name and including the parent directory name would easily disambiguate these. I remember that this behavior was actually present a while ago but the search has been changed to consider only the filename at some point. Maybe you had a reason to do so but I would be nice to bring the old behavior back at least as an optionally configurable feature.
Can be configured, see Settings->Kate->"Quick Open"
Oh, sorry for missing that. The configuration options works as expected, indeed.
Note that this setting has been removed. Once the search term contains a '/' the path search mode is entered automatically.