Browned barrels were commonly varnished. Military specs talk both about varnishing brown barrels, and polishing bright barrels with a piece of hardwood. The US army specifically prohibited polishing barrels with the ramrod. I don’t know why.
I suppose it’s conceivable that you could varnish a bright barrel and be historically correct, although if you burnished it on a regular basis too, you’d probably rub off the varnish PDQ.
Based on personal experience, the smoother the finish, the better it resists rust. The differences are rather striking.