No Mauser expert here.
Interesting rifle to be sure, a beauty in its day and an enigma as to 6.3mm proof stamp (would be BORE not GROOVE) and claimed 7x57 chambering.
6.5x57 maybe? Oversize neck and throat and you probably "could" get a 7x57 to chamber…..

The exterior could clean up pretty well, but that recoil lug inletting looks like a horror show.
Right side grip panel sure has the look of a repaired split thru the grip…..

A guy like Steve Bertram could work his magic to bring it back…..at a price.
- Mike