Same problem for me: the "You're sharing your screen"-toolbar in new teams overlaps the browser tabs.
I know I can restore down my browser, and then click on the tab. All of this is taking 2-3 seconds in total.
BUT: this all is distracting. To the viewers, who wonder about my senseless clicking around. To me, when in the middle of explaining complex details.
If Teams wants to stay with this feature, here a mitigation option:
When the "Pin" mode is not selected, then show the collapsed toolbar (the small one with a height of about 20px).
And show the huge, distracting one, only on mouse-hover. Best with a delay of 500ms.
Remember Pin-setting from last session.