There are currently about 3 million federal employees if Elon and Vivek cut 5-10 % will services be noticeably impacted ? With their ability to automate services I doubt it.
Having read the Musk biography, there are a lot of his disciples that understand the Musk "algorithm" and way he goes about leaning out an organization. I can see teams of people led by some of his trusted leaders going into an agency, looking at processes, job responsibilities, automation opportunities, redundancies, etc., and identifying the waste. You would hope there are a group of people in those agencies that have been frustrated with the inefficiencies and would be on board and support the change and be a part of it.
I don't see where Vivek fits in this as he doesn't seem to have any relevant experience, but maybe he's a mouthpiece and a favor Trump is rewarding him.
My guess is 5-10% is a lay-up.
https://en.wikipedia.org/wiki/United_States_Department_of_Education
Just taking the Department of Education alone - $238 billion budget and 4, 400 employees - mostly student loan management (which has been a disaster with defaults and forgiveness). This can be outsourced and can't be run any worse.