Agreed, no visible signage. According to xgis, Pikk hasn't been modified since 2014 (https://xgis.maaamet.ee/adsavalik/ads?ads_oid=LP00016172 exclude last 2 versions as they are newer than this note), Sulevimägi was last modified in Teeregister in 2020.
According to https://gis.tallinn.ee/veebikaart one-way segment of Pikk extends to Pühavaimu. Im pretty sure i have never seen one-way signs there, but i do have seen even police cars driving down the alleged wrong-way.
Reported errors to both Xgis and Teeregister.

Case with Lai st is bit more clear. Again, no one-way signage, but there's no-entry sign at other end.