Running on a Surface Laptop 3 at default res (2256x1504) at recommended scale (150%) So.not sure if the latest Edge build just fixed it, or if it had something to do with Google Chrome being installed, or both actions combined ? I can repeatedly close/open with touch without problems. Since that point, the touch issue is gone. (It frequently auto updates, so I don't think I've ever too far behind the latest version.) I clicked the update button in Edge, bringing me to version Version 84.0.522.9 (Official build) dev (64-bit). I went into the About settings page in Edge and noticed an updated was available. Re-opened Google Chrome and still no problem there.
I closed Chrome and switched over to Edge (Dev channel), and closed the browser by touch, and the cursor disappeared as soon as I opened it again. I installed Chrome, and Chrome didn't have any issues with the cursor disappearing.
I'm hesitant to say it is fixed, but I can't reproduce as of just a minute ago after having installed Google Chrome to test what you asked about.
