I would suspect the right wheel motor is barely working (or not at all) and forward motion is from the left only so any attempt to turn left is problematic since the right wheel motor has little or no power. If you can get all wheels off the ground you can test and compare wheel motors.
The model number you listed comes up as a Murray riding mower.
Enter you model number at the Toro web site. I believe the manual will have the wiring diagram.
https://www.toro.com/en/customer-supporthttps://www.partstree.com/parts/ also will like have same. Just need the right model number.
ZTR mowers will kill the engine if the operator seat is not occupied and the brake is released. Likely you have a failed seat switch but could be other... it will depend on the particular Toro model.
I would say that the cable has been overtightened and causing the engine to race when it should be idling. Recheck the fitting and the tension of the cable. At idle, it should be barely moving the carby throttle.
it could be a few things but i would start by checking the wire connections at the switch to be sure they are secure and not corroded or broken. also the switch itself may be bad. check to see and replace .
recoil tabs may be stuck or damaged ---try tapping wot a rubber mallet around recoiler and try pulling --or will need to remove cover and look at the tabs
fuel filter, fuel line, more than likely it is still the carb. there are very small holes that have to be cleaned good or it will do as you have said. clean again with carb cleaner and a small wire. blow out with compressed air. should run like new again.
