For the record, the provided link shows osm.org routing with OSRM going on Tallinas street, turning left on Brīvības, taking next right, then right on Cēsu, then right on Tallinas again.
This is caused by the previous incorrect turn restriction.
The OSRM instance behind osm.org is not updated that frequently, and right now https://routing.openstreetmap.de/timestamps/ shows last update being at 2020-11-01T14:00:00Z .
OSRM demo site has updated the data already, and here's the corrected relations at work: http://map.project-osrm.org/?z=17&center=56.962389%2C24.138197&loc=56.962386%2C24.138197&loc=56.964012%2C24.135557&hl=en&alt=0&srv=1 .
I'll close this note - but if there are still routing issues after osm.org-backing OSRM instance has updated, please feel free to reopen.
Thank you so much for verifying and the followup, it is crucial for proper routing.