@lmh that information they provided is outdated. In terms of cookie management, I pretty much touch on it at the two links below:
Just to confirm, you have tested this on Chrome and it doesn’t do the same thing there?
Guess also would like to ask you to try on a new profile in Brave. Go to the hamburger menu 
→ More Tools → Add new profile. This will create a second profile with most settings at default and no extensions disabled. If you can leave things as is on that profile and see if you have the issue as well on that profile, it would be nice.
NOTE
I say most settings at default because any custom content filters in Shields or any changes to brave://flags will persist across all profiles.
Which is perfect and generally what you want to use. Overall would say to keep like I suggest at Helpful Info & FAQ for Brave Users - #28 by Saoiray.