quick answer: add the AutoplayStopper extension —
detailed answer / some history: Brave is built on Chromium. (You may already know this.) Until mid/late summer 2019, Chrome users (and hence Chromium and Brave users) could edit a flag that controlled autoplay policy. Mid/late summer 2019, Chrome / Chromium (and hence, Brave) deprecated this flag. The explanation from Google: enabling advertisers to “engage” browser users. The result: users no longer control autoplay. I installed the AutoplayStopper extension to minimize this “engagement”. It’s worked well for me. When this topic comes up in discussions, I’ve not seen any negative comments about AutoplayStopper.
Mid-May 2020, a Brave moderator suggested Brave may have a fix in the works. Maybe.
Installing AutoplayStopper fixed the problem of uncontrolled videos for me and for others. YMMV.