The 257 Roberts seems to have a 2.775 standardized length, but the parent case, the 7 X 57 has an OAL of 3.071". Traditional American "short actions" are based on the 2.800" overall max length of a 308 Win. Given a 30-06 has an OAL 3.34", I am going to claim that 7 X 57 mm actions are an "intermediate" action.
I have a pre 64 M70 in 257 Roberts. It is long throated, and a previous owner took out the short action parts, so now the magazine box is 30-06 length. I can seat my bullets out to 3.0" if I want, and they feed perfectly well from the magazine. I consider this an advantage as long seating the bullet adds a bit of air space, which can be filled with more powder, to have more velocity at the same pressure, or more powder to +P levels. Either way, I think it advantageous to seat the 257 Roberts to 2.9" in my M70, as that is close to the throat.
Based on what I see, a 1930's or post war Mauser military action would be just the ticket for a 257 Roberts. The magazine box for a 7 X57 or 8X57 is long enough for a long 257 Roberts round. I would avoid WW1 and earlier actions, and I would avoid German WW2 actions after 1942. This is primarily based on suspicions of wartime actions built under wartime stresses by unhappy slave laborer's. The ones at FN pulled tricks such as raising heat treatment temperatures by 100 C, just low enough to pass a proof test on a machine cannon, but brittle enough to ensure it would fail in service. Tee he, tee he. This was very dangerous as when the Nazi's discovered saboteurs, they executed them, and not in secret. They left the bodies hanging so everyone got the message. Arbeit macht frei "Work will set you free!" EEK!
I would not use a 308 Win standard American short action. However a 30-06 length action will work well, just pick one with an integral magazine box. The detachable magazine box guns are designed so you buy, magazine boxes, I don't know how flexible 30-06 length magazine boxes would be to short rounds. You know, something like a 60's, 70's, 80's, 90"s M700 ought to work out fine. Anything with a 30-06 case head and a 30-06 magazine box. A push feed M70 in a 30-06 length cartridge out to work well. You have lots of options.