Drove 2wd tractors for over 50 years before driving my first 4wd tractor, and using turning brakes to make a short turn on a slippery surface was and still is automatic. But the first time I tried it with the 4wd engaged the resulting noise from the front end told me it was a very, very bad idea. Now, I don't use turning brakes on that tractor even when in 2wd.
Just remember, your manual was provided by the folks with high dollar replacement parts for you.
Turn however sharp you need and leave it on unless going a long distance on paved surfaces, for safety. No 4WD? 2w brakes, only on rear. You'll skip going downhill.
Running in 4 on trucks, on hard surfaces, wears ring and pinion out. I've seen it wear them out or shear the bolts holding ring gear to diff. Seen both many times.
My understanding is that the front wheels on a compact tractor are geared to run as much as 5% faster than the rear wheels. This tends to put things in a bind on hard surfaces such as pavement.
2wd will lock the inside rear wheel, so all power is to the outside rear. The inside front does not stop in a turn (it is slower than the outside, but not to the degree of the rears). Using brakes as a turn aid on 4wd with open front diff will cause the outside front tire to rotate too fast, and the inside front to drag, creating wear on the drive train and tires that is not value to work. I THINK, that is why I only use brakes as a turn aid with or in 2wd. I do look forward to a definitive answer if I am off.