Yes, they are correlated ; contracts are created with budget authority afforded to federal employees. Essentially the only way to get promoted is to amass reports and budget, and use it in some way.

So it’s basically like this: yes, the federal government creates jobs and the cost of those jobs directly is only 5% of the budget. However the real cost of those jobs is in spending, in terms of opportunities they champion, which essentially amounts to all discretionary spending conducted by the federal government — ~30% of the budget.