There is already a discussion in the community "Brush Outline/Circle disappearing intermittently (NOT CAPS LOCK) ". But since I have figured out in detail how to reproduce the behavior and when it becomes present, I want to report the issue officialy that Adobe hopefully will fix this in one of the next upcoming patch releases.
Win 10 Pro 64bit 21H1
Adobe Ps 23.0.2
The issue is only present in combination when using Masks on a layer!
Create a new document (white, black or transparent layer)
Add a Mask to the layer
Select the layer OR the mask (independent on what you want to paint)
Select the brush tool
Try to start moving the mouse quickliy and pressing the left mouse button nearly at the same time and keep the mouse button pressed
Try to repeat until the you get locked in the issue and the brush circle disappears and the mouse arrow becomes visible
When working with a mouse as input device, the chance to facing this issue is probably rare because this kind of operation, moving the mouse and clicking the button nearly at the same time is kindly unnatural.
But it looks different when using a pen tablet as input device, because now it becomes a more natural operation when hover the pen toward the tablet surface and then drop down onto the surface to start painting.