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Yes, there are advanced stability control systems that incorporate throttle with braking. I really doubt the OP is going to do that kind of coding and controls with his home project
The difference between fuel on and fuel off engine braking is small - but it can be enough to make a difference in the right conditions. That is why you wouldn't want to set the engine to always turn off when the throttle is lifted fully.
When I lived in TN our neighborhood was up on a hill. It had an 18 degree drive up from the main road (yes, I measured it with an angle finder). With our truck in 2wd mode that hill was dangerous to go down in the snow. If you let off the gas too quick or too much the engine braking was enough to break the back loose and you wouldn't gain control again. Sideways slide down the hill into the main road. The only way to safely descend that hill was to go down in 4WD low and just let the truck idle down the hill or chain up and drive down - then unchain at the bottom.
A car with an automatic will only start the engine in neutral or park. It has an interlock to keep if from attempting to start in gear and having the starter propel the car forward. A car with a manual transmission will only start in neutral or if the clutch is disengaged. It has an interlock to keep from attempting to start in gear and having the starter propel the car forward.
Same with a homemade mild hybrid system. You wouldn't want it to start the car in gear with just a touch of the throttle unless it is in neutral or the clutch is disengaged.
You mention twice about adding a switch to decide when to active the stop / start. It would be easier to tie into to the neutral switch. Shift to neutral - the engine turns off. Shift back into to gear - the engine turns on when the clutch starts to release.
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