looks indeed like a 7x57 without rim
the 32/40 looks like it could not compete against the bigger rounds.

the 8x50R Mannlicher ( not Austrian because you had to name it than Austro-Hungarian) was just at hand when they need a new cartridge after the ban of the 303 so it was there to do that. just as it indicate by the name it became the ".315 india" only. if they had found another cartridge before for the job the .315 india will be looking different today.
an interesting historic similarity is the french Rival rifle offered in 8x50R Lebel, 303 Brit., 375 Flanged and 405 Win, only the 7mm is missing.

in the end only the mauser can survive