One thing that helped me get past this feeling was looking around at other desks and realizing that either a. no one cares what you are doing because they are too busy working on their own stuff or b. half the office is watching youtube anyway.
While this is hardly an unknown fact amongst HN readers, a lot of people get very surprised when told about this.I've seen some of my colleagues going to private mode to browse something not work related, and when I explain that tbis won't help at all, they are almost shocked.
As someone who actually works on the IT-side of this, your statement is technically correct but my experience suggests a vanishingly-small number of employers actually monitor this data in any rigorous way. The only time I've ever seen an org reviewing web logs was in response to a specific formal HR complaint.