Cut rifled barrels were/are stress relieved like anybody else's. A difference between rifling processes is the stress introduced, and what is done to better the barrel BEFORE and AFTER rifling.
~15yrs ago I shopped for a barrel and asked many button barrel makers how they address contouring in their process. Most were unaware that either contouring needs to be done before button rifling, or total stress relieving between rifling and contouring, else the bore opens at the muzzle. Then you get into what lapping does on top of it. None actually measured bore dimension, and none would guarantee anything real about their barrels, not even the correct twist rate.
At that time I decided that button barrel makers were doing no more than divvying up the cheaper barrel market.
There are better button barrel makers today, some mentioned. If I were you considering any today, I would investigate details of their process as I did, no matter what our mob claims about them..
Another barrel maker not mentioned is Loather Walther. Sadly famous for hammer forging, and god awful hard steel, yet more capable than any and all other barrel makers in existence. In fact, if it can be done with barrels, LW can do it. Any rifling, any lapping, any steel, any process, and actually capable of measuring and manufacturing to prescribed bore dimensions. This is not the same as merely air gauging to validate tolerances.
Hammer forging in itself can also have it's advantages, in that a heavily contoured hammer tightens at the muzzle with heat(opposite of buttoned). Tightest at the muzzle is essential for accuracy, and nobody knows this better than LW, who offers a separate accurizing service to ensure it.
I've never ordered a LW, but will some day.
I always consider stress, a contouring plan, lapping needs, and intended field use.
And every finished barrel of mine from now on will be melonite treated, as barrel life is just too important to dismiss.
With this, I guess I'll never end up with a Proof Research barrel.. They will not allow it.