motorcar is widely used but the key includes all kinds of vehicles
it doesn’t, or more precisely, it includes other motor vehicles with 2 tracks when used as an access restriction but doesn’t when used as a permit/positive. Not really transparent, but this is how the tag is used afaik (and also how traffic signs work around here).
Curious example: https://www.openstreetmap.org/way/33053073#map=14/41.8336/12.4545
traffic sign is vehicle=no except cars (vehicle class). Funny enough with these signs you might legally walk there.