If anyone is still trying to figure this out, I found this in the comments of a reddit tread, and it does work!
- Right Click your Brave Shortcut
- Go to Properties
- Add * -disable-features=DownloadBubble* (without the * symbols) to the end of the Target Field (after the ") there needs to be a space after " and before - for this to work
- Apply changes and Launch Brave
- To pin to taskbar first unpin your current shortcut
- Right click the modified shortcut and use the pin to taskbar button