The German destroyer Z-39 in the photo above finished the war with a pretty decent light AA suite.
another photo of the same area.
USS Z-39 (DD-939)/ Ex-German Z-39) showing after 37mm Bofors-type A.A. gun platform, near the after stack. Note these 37mm guns are of two different types. Taken at Boston Navy Yard, August 11, 1945. Courtesy of Robert F. Sumrall. Source: Naval History and Heritage Command, Photo No. NH 75405.
The shrouded twin mount (and it's sister on the other side of the funnel) were the old manual loaded guns. the guns just forward were the newer automatic guns.
however there there were a further eight of the new guns mounted. Two twins just forward of the bridge behind A turret and two more twins (one on each side) just behind the aft bank of torpedo tubes. the 20mm AA battery appears to be one twin mount on each bridge wing and two quads back to back above X gun.
picture from the stern
The main guns were pretty much useless for AA fire. (my opinion) because they were 15cm guns with low rates of fire and for the single mounts low elevation. The twin mount had 47 degrees of elevation but it's elevation speed, traverse and rate of fire may have been lacking.
I would note that in order to mount this AA battery one 15CM gun has been removed from the after deck house where it pointed forward over the aft torpedo tubes.
I have no information on when the 15cm was pulled and the extra Flak guns installed.
Information on the Navy 37mm Flak/42 is a bit sketchy. it is
said to be developed from the army 37mm Flak 36/37 but with a bit longer barrel and a higher rate of fire.
The old Army guns used 6 shot "clips" fed in the side, the Navy gun used a 5 shot (?) clip fed in the top. The fast firing Army 37mm Flak 43 used an 8 shot clip fed in the side.
I have no idea why the Army and Navy adopted different model guns using different feed systems and different ammo. The navy did use some of the Army 37mm Flak 43s on some ships.
There may be some dispute about the rate of fire of the 37mm Flak 42. Anthony Williams book says 160-180 rpm not 250rpm. 250rpm is correct for the Army Flak 43.
Since they used different ammo, used a different feed set up and had different length barrels it is a bit difficult to believe they had identical rates of fire. However 4-5 times the rate of fire over the manually loaded guns is still a very significant improvement. (I have a hard time believing the 30rpm for the manually loaded gun for any length of time or in bad weather)