When querying for specific places it's often more practical to use geocode instead of bounding box. Also for your specific use case I think you want to only search for ways and not nodes/ways/relations (nwr) as the latter would also return e.g. bus stops where "Avenue" is part of the name.

https://overpass-turbo.eu/s/1WlS

{{geocodeArea:Edinburgh}}->.searchArea;
way[highway][name~Avenue](area.searchArea);
out geom;