Same issue. Few days ago completely moved from Chrome to Brave over this and everything worked fine until today.
Issue still present when in shield setting i chose to aggressively block trackers and ads.
Brave Version: 1.58.137
Working System: Windows 10
Well but going on the Store I should see the new version but till now there isn’t. And now even AD-Blocker on Chrome ceased to work. YT blocked the videos.
Something new I learned, when you have the shields up while on YT, you will not be able to view notifications or if you have another google account, you can’t switch accounts unless you disable the shield in Brave. Hope Brave comes up with an update to the browser soon about this.
facing the same issue, tried updating the components also as stated by someone in comments but that also didn’t work. Only way is to open youtube in private tabs which is annoying. Just waiting for some smart brave developer to come up with something.