I repeat.
Mackie told you that the output from the alternator should be 30V AC if the alternator is working.
You have just replaced the rectifier without checking if the rectifier was working.
Checking the battery voltage is a good place to START.
If it is too low then the next place to check is the rectifier voltage.
You check for DC output from the middle terminal to earth.
It must be 13V to 15V
If not then you check the AC output from the stator.
They will be the 2 wires that are the same colour measure between them 26V AC to 40V AC
And from each one to earth , must be the same voltage AC.
If the AC readings re not within spec then the stator is the problem
If the AC measured good then the rectifier is the problem.
IF the AC & DC measured good then the problem is in the wiring.
So you check the voltage from the rectifier all the way back through the loom.
If for instance the wire is broken just at the terminal plug on the ignition switch, replacing the switch will not do you much good.
The mower shop near hear has a thing for cutting the rectifier wire and connecting it directly to the battery via the hot terminal on the starter solenoid.
As you have no idea what your shop did, you will have to check everything.
This applies particularly if they decided to use insulated crimp terminals in a place where they should never be used - in an exposed position.