DOGE isn't a source so don't cite them. They just made shit up.
The American public is stupid and wrong and their perception is not useful here. They will believe the government wastes 50% of every dollar because they have been told that, even though it's just stupidly wrong.
The GAO is actually the only information you provided. They are trustworthy and happy to be critical of every administration, and they don't get enough love for their important work.
I don't know if you realize this, but 3-7% literal fraud is actually a pretty good number for a very complicated system. 15% "waste" where it's hard to even define what "waste" is is also a good number.
Visa and Mastercard accept far higher for a far simpler fraud profile.
Also you said "This guy thinks waste in government is only 15%" and then the only data you provided has to wave many hands to get up to 13-20%. What the hell man?