Since Nominatim doesn’t index route relations at all, I presume you’re referring to something like the OSM Relation Analyzer’s search box? Under the hood, this tool generates pretty simple Overpass queries that, indeed, would be unable to distinguish various relations within a route relation hierarchy. It doesn’t expose keys we’ve been discussing like direction=* and `is_in:state=*``, but I think that’s a pretty tractable problem to solve.
Or if you’re referring to JOSM’s function for searching already downloaded elements, I think that gets into the proposals around putting human-readable disambiguators in description=* or disambiguator=* and expecting editors to surface those in addition to name=* and ref=*.
What I meant is that wikipedia=en:U.S. Bicycle Route 50 is easily distinguishable from wikipedia=en:U.S. Bicycle Route 50 in Ohio just by looking at the tags. It’s just a fragile workaround, that’s all.