Consider keyboard remapping:
FYI:
https://docs.microsoft.com/en-us/windows/powertoys/keyboard-manager
So when "Cycle Profile" is pressed the resulting keyboard output is altered to Cycle DPI.
Powershell may be another available option:
https://superuser.com/questions/600675/how-to-remap-shortcut-in-powershell
You will need the applicable keyboard codes for Cycle Profile and Cycle DPI.
Then a bit of script to recognize Cycle Profile and when found/received, replace with the code for Cycle DPI.
Here is a link that explains making the required change for a Logitech G900
https://www.sleewee.com/how-to-change-dpi-and-set-dpi-shift-in-logitech-g-hub/
Not a directly applicable link per se. However, the link may provide some terminology or other information that you can use to seek similar information for your RAT 8 mouse.