The online degree is a legitimate degree conferred by Harvard University, and you will earn the right to claim whatever is printed on that degree, same as your Berkeley degree. I think your trouble is caused by the verb you want to use. You want to say, “I went to Harvard.” Instead, you say, “I earned my (name-of-degree) from Harvard.” Your resume will not use “went,” it will simply state what’s printed on your degree.
I started a thread several years ago, Harvard Through The Back Door, discussing how people viewed the Extension program, not the program you’re talking about, but the underlying issue is the same.
Our son is now living in MD finishing his master’s online from Georgia Tech. He attends real-time classes via Zoom and works on projects in teams and confers with his classmates and professors via Zoom, phone, chat, and e-mail. His diploma will make no distinction as to the method used to complete the program as walking the campus is not a degree requirement.