We have `amenity=brothel` but that's not a good fit imo. The wiki says it's for an "establishment." Nonetheless there are 16 occurrences worldwide of `amenity=brothel` + `brothel:street_prostitution=yes`, so it seems that's the most popular solution.
If it feels wrong (it's verging on "troll tagging"), you could just go with `prostitution=yes`, also in use. (Probably as a property of a bar or hotel, I'm guessing, so maybe the standalone version would just be `amenity=prostitution` -- but it seems that tag is not yet in use anywhere.)
Regardless, these tags would no not go on the street itself, but rather on a node or area (or multipolygon) to the side.
JJ
edit - If you do map something like this, it's likely that another mapper might remove your addition as unverifiable. Consider adding a `source` tag with a link describing the regulations that permit this activity in this area, if possible. If the area is signed, describe the signs in your changeset comment.