This possibly caused by the PS2 mouse emulation performed by the BIOS. Since deep sleep mode is essentially turning the laptop off, the BIOS will try to detect if the OS is using the touchpad when you wake it up, and if not, will go into emulation mode. Since it may take a few seconds for the OS to wake up and start using the touch pad, the BIOS may prematurely decide that emulation is necessary. The result will be that you will (depending on the OS and settings) get no response, because the OS is not looking for a PS/2 mouse, or you get a response, but the functionality is different and degraded, because the OS thinks you replaced your touchpad with a PS/2 mouse while it was asleep. I can confirm that this does happen on my laptop running Pop OS (which is Ubuntu based) when deep sleep is enabled. It seems to be fixed 100% since I disabled PS/2 emulation in the BIOS.