You now need to check the red wire circuit after the valve for the (less likely) possibility that the ground/short is not inside the valve mechanism..

Very likely you now need to hire a pro who will
carefully evacuate, recover and store the freon (R-22 now very very expensive )
fill the system with nitrogen,
then replace and solder in the new valve,
check for leaks,
evacuate the nitrogen,
refill with either R-22 or a “green” substitute like MO99.

Looking at $$$ unless the electrical problem is not in the valve.

Do not be surprised if the pro advises replacing the whole system due to age, parts availability. and R-22 laws.

If you read up on whether R-22 really damages the Ozone layer or is significant as a “greenhouse gas” compared to methane or carbon dioxide, it will leave you angry.