How can I hide the Quicktime control bar during screen recordings if I still need to use my mouse during the recording?

How can I hide the Quicktime control bar during screen recordings if I still need to use my mouse? Prior to the last update, I could hide it by simply moving the control bar off of edge of the window that was being recorded and it would remain hidden outside of the recording "window".

However, since I updated to macOS Tahoe 26.4.1, this no longer works.

The control bar is more persistent. It does fade after a few seconds but I can't move it out of the way - it keeps fading and then reappearing every time I move my mouse.

I do need to use my mouse during the screen recording to "point" to items on the screen, so hiding the cursor isn't an option, either. Help, please?

I'm using Quicktime to screenshare my iPad (A16) during Zoom meetings, if that's any help. I know I can share via screen mirroring but it's harder and not as reliable.