The WW1 era 7.92X57S used a 154 grain bullet at around 2800+ fps.
The WW2 era 7.92X57 standard ball cartridge used a 196 gr bullet.
The heavier bullet gave better penetration of obstacles and better energy at longer ranges. I think they were mainly interested in a cartridge suited to the MG34 LMG with infantry rifle use secondary.
Early in WW2 German Infantry were issued one five round stripper clip of Tungsten Carbide core AP ammo, for use if pinned down by allied AFVs.
The standard target ammunition for the CG-63s was originally a 140gr Boatail bullet with a muzzle velocity of about 2,600 fps.
A similarly downloaded .30-06 cartridge was used by some South American police armed with the short barreled .30-06 Mauser Police Carbines. The muzzle blast and recoil of the full house .30-06 from an 18 in barrel being too much for police work.
Balistics were similar to the .30-30.
These same downloaded .30-06 cartridges were also used at military or police academies for target shooting with the full length service rifles on 200 yard ranges.