I have cut through berms, but never constructed one. But this project strikes me as wrong. You could do it, but I fear that once it is done the people who would hire you would then realize it was a mistake and will blame you.
With a base 10' wide and the berm 4' high you are looking at having the average slope on both sides almost 45 degrees. Is the berm to be grass and mowed? Not easy to mow at that kind of slope, especially with the trees or a fence it would still need on top to block the view from the road.
I think a better, and less expensive, option would be construction of a privacy fence along with trees.
4 feet high, stabilized, with a drainage plan for both sides of the berm and removal of existing plantings and replacement with new plantings, correct? Does the community (or the owner's insurer) require permitting for landscaping that results in any change to the storm water drainage plan? If yes, have you factored the time and cost? Some communities want new engineering studies for this kind of thing. Not cheap.
This looks like a narrow space for that high a berm that close to the house. If the objective is privacy, it seems like a fence would make more sense. If sound reduction of tire/traffic noise from the road is desired, a masonry wall would be better. A berm seems like a bad plan here.
I built a pond once, 650ft dam 30ft tall. Looks like sort of a berm there under trees now just short. So they wanna build that up put the trees back in. Super doable job. Use the skid loader to drive the soil in as you build your berm. Shaping it as you go, 4 to 6in thick driven hard to pack. You'll be in upper 80%, lower 90% compaction, even more if your layers are thin. Slope down to the ditch, and down to the edge of the yard, done. 4k is good price, might go up a touch. Keep help home till dirt work done.