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.
more Brave-specific details: Autoplay media popup discusses toggling Brave’s Autoplay setting available here: brave://settings/content/autoplay and brave://settings/content/popups I found toggling either / both of these options failed to stop Autoplay — specifically — on finance.yahoo.com — the site about which you’re enquiring. AutoplayStopper does block autoplay on finance.yahoo.com Brave’s autoplay blocking options don’t.
The downside to AutoplayStopper: broadly speaking, extensions (any extension) are risky. Further, NO Chromium or Chrome-based browser gives users control over extension updates. Good extensions go bad. Some details here:
3/1/2020: The Case for Limiting Your Browser Extensions
11/20/2020: Abusive add-ons aren’t just a Chrome and Firefox problem. Now it’s Edge’s turn
2/5/2021: A 0-day, malicious extension, and sync abuse are keeping Google developers busy
and 3/1/2021: Is Your Browser Extension a Botnet Backdoor?