squeezing the mouse a bunch fixes this. The root is the thumb button is by default a gesture sensor. When the gesture mode is active your cursor freezes in place while it tracks internally your movement. If you disable the button in the logitech settings it will never freeze your cursor again.

As suggested by Nabeen - pop the bottom panel off (screws under the left and right pads, two exposed at the top), find the small circuit board below the thumb piece, and loosen the screw.

There is a small circuit board that houses the thumb button. Over time, the screw becomes too fight and so the button registers as boing constantly pressed. To fix this, open up the bottom panel, locate the screw in the circuit right below the thumb button and loosen the screw by half turn.

Did some food got jammed in your thumb button? It could be fixed with opening the mouse, or just removing the lodged particles?

A possible workaround (not fix) is to disable the thumb button entirely in Logitech Options app. I did this to solve accidental presses during games.

You can gain access to fix the thumb button by peeling off the pads underneath to get to the screws and remove the base. Inside retighten the button assembly in place. New pads can be purchased online.