Virginian,
You are right. The only "correct" way to weld something like this is to weld, stress relieve in a heat treat oven and re-HT. But that's impractical. So, it's a choice of two bads; whether to leave a weld with obvious high stresses and hardness or 'seat of the pants' normalize it. You may recall, this assembly of barrels is silver brazed at the chamber end. I'm guessing it was done with a torch in 1900. Also, barrels on the vintage guns I've worked on were of very low hardness and heating them wouldn't likely lower strength significantly. It's common to stamp maker names and engrave scroll and gold inlays into the outside of a barrel chamber, which is probably as an bad a thing to do as welding this area.
One additonal thing, I TIG'd a sleeving job on a LC and had hard welds/adjacent areas and had to torch normalize it or figure out how to cut the chambers with something better than HS steel reamers. From personal experience, I can tell you the barrels will have spots hard enough to take the edge off a Clymer HS steel reamer if you don't normalize. In that bottom pic, I'm about to remove the edge on that $180 Clymer reamer. Fortunately, I have a friend in the cutter manufacturing biz and he had another friend specifically in the reamer biz fix the forcing cone portion that got dulled.
BTW, metal specs were nearly non-existant, proprietary formulas in 1900. You won't find 4000 series chromolly (todays common barrel material) until the War years, WWII if I recall. Serious efforts to standarize metals in the US happened in the period just before and during WWII.
