Not sure why you say “thick”, it’s most likely a normal, typical, bullet jacket of the time. And as being steel would take a magnet as only a thin layer of CN over it…
As some of these are loaded with FMJ bullets I’d think those were more likely military than this, as it is designed to expand.
Yes the case is a military headstamp but rather than have new cases made with a non-military headstamp, the retailer/factory/or whomever used what was on hand. You see .303 inch cases with military style headstamps loaded with soft nose bullets don’t you?
This M-93 Mann. must not have been widely used as the rounds are not often seen & when they are a good portion are loaded with sporting style projectiles. At least that’s my best guess about them.
Note the date on the Fraser bullet case, 1903, almost the same but for the jacket cuts, so for sporting use.