I want to draw on all over the screen and not just on a single screen or app. Is there any mac app that does this?
You can use Presentify. It lets you annotate your screen and also highlight your cursor/mouse. You can draw over anything, be it images, pdf, browser, videos, and the list goes on. The app is available on the Mac App Store.
Mac App Store: https://apps.apple.com/app/presentify/id1507246666
Demo: https://youtu.be/CTR1iAbGhjg (this video is of an older version, the newer version has a lot more features)
I hope you find it useful.
Disclosure: I am the developer of the app.