I was looking for an answer to this also and came upon your post. Looks like there is still no settings option yet, unfortunately, but hopefully soon. In the meanwhile, there's a workaround you can do with inspect elements to hide the recent activity. This only works for the tab you are in, and you'll have to do it again if you open a new tab, but may be helpful if you have to share a screen.
Steps (example here):
1. right click
2. select "inspect elements"
3. In the inspect elements pane, select the option for
<slot class="side-panel" name="side-panel">∞</slot> flex == $0
(if you've selected it correctly, then the area will be blue)
4. Right-click on that line and select "hide element".
Hope that helps in the interim.
