More likely to be a 6,5x54 Mannlicher Schoenauer, for use in a pre-WW II MS M1903 Sporter.
.276 cartridges came on sale (thru DCM) after WW II, and I have an “American Rifleman” from 1947 or 48 article on building a hunting rifle in .276 Ped, to use up all this excellent surplus ammo. Others obviously saw the close connection in dimensions, with the 6,5x54MS ( the metric designation of the .276 is the 7x53), and so resized the cases to 6,5MS, with excellent results…some other enthusiasts also made Bolt actions using the .276 as a long range target cartridge (using a Springfield 03 or a commercial bolt action (Win 54 or Rem 30). Barrels and Chambering reamers for .276 were also offered up to the mid 1950s…until all the ammo dried up and was shot away, dismantled, or otherwise used up.
The cartidge in the Picture looks like a dismantled case, resized, as the Crimped Primer looks original GI.