The standard chambering for the M1910 is often referred to as 9.5x56 MS, or in British parlance, the .375 Rimless Nitro Express.
Interesting discussion on whether or not the rim was included in the Austrian measurement.
If the bore is good, this would be a very worthwhile restoration.
They are marvelous hunting rifles for the larger medium game such as boar and bigger stags. Absolutely love mine!
You might remember a hunting anecdote I posted some years back.

Thought it might be a take-down, by the "hook" under the rear tang, and that banded loop under the barrel (assuming its not a sling-swivel attachment?) ,,,but no lever in front of the trigger guard.

Congratulations on your great buy!