So, I’ve got a scrubbed and sporterized Mauser of the 98 style that was most likely a former military rifle. It has what looks to be a small ring receiver, and I believe it to have been a Kar98az at one point in the past. It bears the remnemtns of what looks like a Prussian eagle, plus some of the small parts are imperial stamped. Assuming I’m correct about it being a Kar98az, what kind of barrel threads should I expect if I removed the current 8mm barrel in favor of say a 308 or 7x57 setup?

Can't remember the od of the shank but the threads are a 1-12 pitch.

Same as the large ring just smaller od.

1.10"x12 TPI

If it's what you say it is (Kar98A), thread would be 1.100 x12TPI 55 degree Whitworth. OD of the small ring receivers is 1.30" .

Small ring shanks are .980"X12 TIP. Not 1.1'" 1.1" is the Large ring size

I have rebarreled two small ring Mauser 98s (one German and one Polish), and both took the standard large ring 98 barrel threads.

In this case, 1.10x12 is correct because he has a Kar98a. A small ring, LARGE tread receiver.

I would avoid the 308. If you are hell bent on a 30 cal, the 300 Savage would work.

The Spanish "Guardia Civil" small ring rifles that were sold as ".308" years ago were actually chambered for 7.62 CETME. It's a virtual clone of the .308 but the chamber pressures are a lot lower on that round. My grandkids stocked their mama's freezer with venison for years with a sporterized rifle I built for them, using 130 grain gas checked hard cast bullets and loading data for a .300 Savage. It's still with one of them, and still taking deer.