First thing I do is see if I can figure out how many times that brass fired.
New brass fired once fo sure, body die plus collet or bushing neck size.
If I'm going to anneal I do it right away, first thing, dirty oily brass with a fired primer still in place.
I want to clean off the discoloration as I work and clean the brass.
I anneal mine dead soft, then work the hardness back into it with one stroke in a FL sizer die with ball expander. That gets me pretty close to factory neck tension, a bit lighter than factory. On my 8mm Mauser that process gives the rounds have enough neck tension to flatten the lead soft points with recoil and not set back. They're loaded a bit hot.
For brass that's been fired unknown times and makes noise when sized yeah better dead soft it and FL+ball expander it.
The military wants the discoloration as proof the shoulder stress releasing step wasn't skiped. The military wants annealing as insurance against a shoulder separation, where the shoulder breaks off because of due to residual metal stress and renders the gun in operable.
I Had it happen to me once, my 30-30 had a shoulder speration when firing new Remington ammo, back in the early 2000s. I didn't know what had happened, all of a sudden I couldn't chamber another round. The gun went bang and recoiled like normal so it wasn't no squib. Lucky for me the cleaning brush pushed the neck and shoulder out, found the decapitated case later.
Weird thing is I never anneal 30-30 brass and have never had a shoulder separation since then.
