Cookie appears to remove browsing history, as per my settings. However, if Safari is opened again, and "show history" is selected, within 3 to 5 minutes, all or most history appears again. Using Safari's "clear history" will remove all web icons, so I do not use it. Manually selecting all history items, then deleting, seems to work if you repeat the process several times by closing and re-opening Safari.
Also, the alert from Cookie that unwanted data has been removed takes several minutes.
MBP, 2016, 16GB, OS 10.15.7, Safari 14.1.1