I have a .360 2 3/4"black powder express that has a paper covering over what is a coiled brass case. It looks to be similar to yours. Definitely not a nitro express.
Looks like a .360 black powder express & not a nitro express as Sportclay notes. These Boxer / coiled cased examples exist in two lengths the 2 3/4" which I’ve only seen with a paper exterior, and a 2 1/4" length which exists both with (some even have case wall print) & without the paper exterior.
I don’t see any trace of paper on your example so I’d say it was as it now is.
There is a drawn brass case which is 2 7/16" long and the 2 1/4" case will be found as black powder, nitro for black powder, or full nitro loads.
Plus gallery loadings and for Fraser rifles (<-often with a different bullet weight than Eley, Kynoch, or a European maker would offer).
(edited once to make it read better)
In the pic it is hard to see but the bullet is a hollow point with a piece of wood in it.
wood in the nose is perfectly normal, & quite typical for the .360 BP Exp. Probably a square piece of wood?