Yes, package formats affect browser security.
I’m unaware of any potential security benefit Snap could provide to Chromium-based browsers, no one has ever mentioned it as a selling point before so my assumption is that there is none. Brave warns users against using the Snap as it still has bugs, so if anything I’d lean towards it being potentially more risky. I’d install it natively and look at hardening Brave. Also check to ensure it is running in Wayland, the last time I used Linux it defaulted to Xwayland.