Honestly since it’s brown bears…definitely bring the firearm. When walking through the wild (if you’re not hunting) wear bells, multiple bells, or something that makes noise when you walk. It’s important to carry multiple objects. There will be a rhythm to the sound, but multiple objects clanging together can break that up a bit, and be more recognizable as a “pace” from something moving. That sound will alert predators that a human is coming. If you see a bear (and have the option) keep a big distance, and holler something like “hey bear!” Don’t shout, don’t sound aggressive, simply a loud “hey bear!”. If a bear becomes aggressive, and doesn’t move away - do what you need to do to protect yourself. If that means firing your weapon, so be it. The wild isn’t necessarily a place you can be safely simply because you want to be peaceful. Be careful out there. I always carry a knife, and have been taught how to use it to protect myself against animals. You won’t always get a choice, sometimes they make it for you. If you cannot protect yourself, because you have no weapon, spray etc, and the bear is clearly going to attack you - drop to the ground in a fetal position, and lock your fingers around the back of your neck. It will be the only thing you can do. Running is pointless, and so is climbing, or swimming. Any of those activities will guarantee that the bear pursues you.
But above all pay attention, carry a weapon, make noise, and stay away from bears near fish spawning areas in season! They’re in feeding mode, and have a greater risk of becoming potentially aggressive.
Wish I had nicer advice, but I grew up around large black bears, they’re smaller than a brown bear. and not quite as aggressive (but they can be!). They are easily one of the most powerful predators I’ve encountered. Personally they’re tied with a mountain lion in my book. Simply animals not to mess with.