Test it for hardness with a new fine file. If you can file it, and the file does not skate, it does need hardening. Replacement frizzens are not always plug and play. If delivered drilled and hardened and tempered, you may or may not get a good fit to the pan. If not drilled and hardened and tempered then experience is needed.
Deep case hardening is a very good choice. When I’ve done pack case hardening I wrap the parts with 1/16” thick soft steel wire, which comes in a roll. If all went well, when I pry the wire off it snaps because it is hardened through and through. That indicates deep case hardening. I temper at 450 degrees for an hour then re-temper the toe to purple/going blue with a torch.
I've done the half soling as well. The frizzen must be ground back at least the thickness of the sole. I’ve used file steel and 1095 as a sole. Not a trivial operation.
Brad Emig of Cabin Creek tunes all sorts of locks. Not cheap- skilled work is not - but great results are reported.