No, Surfshark doesn’t log your browsing activity. It has a strict no-logs policy that has been independently verified. Surfshark doesn’t keep records of any of the sites you visit, the videos you watch, or the files you download.
Surfshark has RAM-only servers — this means no data is ever written to a hard drive and all data is wiped every time the server reboots. This helps ensure that none of your internet activity is obtainable by hackers or snoopers.