I believe browning of metal is often way over done. The original formulas I’ve used, and seen used, alway refer to the brown as a plum brown, and as a clear semi-translucent finish. Most browning jobs today are dark, and anything but translucent.
I have examined parts that are black, and assume these hand forged parts are coated with linseed oil after forging. That would be the way an old time blacksmith would likely prevent rusting. I have not seen this finish on a barrel. All black, or dark grey colors on a barrel that I’ve seen, seems to come from a rust blueing process.
Hungry Horse