Actually, annealing softens the brass so that working the brass when sizing the case won’t cause cracking. That’s what creates a discoloration of the cases.
".... so that working the brass when sizing the case won’t cause cracking." No. Strain hardening does not cause immediate stress corrosion cracking (season cracking) all by itself. Long term exposure to corrosive atmospheres causes the differential cracking along the material grain boundaries
"That’s what creates a discoloration of the cases." No. Strain hardening does not cause the discoloration. The blue/gray discoloration is simple oxidation of the copper alloy shell case induced by the approximate 1000 degree F temperatures of the annealing flame or induction heating.