FWIW, with apologies for duplicate content if the google search includes any of the following, all versions of Brave Browser in macOS create their own folders in your home folder (/Users/YOURUID/Library/Application Support/Brave Software). I have Release and Nightly installed, so mine looks like this (click image to enlarge):
Your profiles live in those folders, and usually unless you create a new profile with the manager, it’s just “Default.” For example, in my Brave-Browser-Nightly, the profile I usually use is Default and is the most recently modified folder, and I have several others in folders the browser cleverly named Profile 1, Profile 2, Profile 3, and Profile 4, as well as a backup copy of Default that I made in February (click image to enlarge):
Your bookmarks, settings, and extensions are stored in your profile folder, as you’d expect. In the Extensions folder, each extension has a folder named a bunch of gobbledy-gook, which, if you’re so inclined, you can identify by going to the extensions’ settings in the browser and noting the gobbledy-gook for it in the address bar.