On my end, it doesn’t do what yours do. Please note that I install Brave to ~/Applications (user home), not in the system wide /Applications folder.
To demonstrate, I start afresh: First, I deleted ~/Library/Application Support/BraveSoftware fold to null out any previous settings and delete Brave from ~/Application. Reinstall Brave from the downloaded dmg into my ~/Applications folder. Watch my screen recording, you will see I install Brave, open it and see the BraveSoftware folder created in ~/Library/Application Support (look at the Finder window on the left side of the screen). Then I visit 75one.cn, you can see I don’t get the “Flash was blocked…” warning icon at the far right of address bar, to the left of the lion face. (You see the translation prompt pop up). So it’s behaving differently from yours. I then went into settings and change Flash to “Ask first”, refresh 75one.cn, click on the site settings and change Flash to “Allowed”, refresh, still Flash not working
My screen recording: https://imgur.com/gallery/5B7S9ZU. (sorry for the low quality, that all I can upload there)
(FYI: I cannot upload screen recording here: 1) was denied because “new user”, 2) this site do not accept .mov file, only mp4)