Took a while to track things down but here it goes
The model number you posted appears to be wrong or at least not recognised by any of the sites I have access to
However there is a model 13APA1T256 from 2017 and using that with the serial number in the Cub Web page found file Number 769-10043 which is the parts book for your mower.
Pages 58 & 59 show the wiring schmetic for the 2 versions of your mower and prove conclusively you only need 1 functioning brain cell now days to draw a schmetic diagram now days and absolutely no functinal knowledge of how to draw a wiring diagram is an absolute necessity.
However if you care to dig it out and open the file you will see that the seat switch is connected directly to the magneto , that is of course after you magnify the diagram 400% so you can actually read the printing to work out which switch is what .
Now if you have the electric PTO you will see the magneto can be grounded by the ignition switch , or by the brake switch + the seat switch .
So if the parking brake is off and there is no one in the seat then the magneto will be grounded.
If the parking brake is on then the seat switch is isolated from the magneto so can not ground it .
The second set of contacts from the seat switch , go into the logic board and shut off the PTO if you are not in the seat.
In any case for the engine not to be sparking both the Parking brake switch & the sea switch need to be faulty which is most unlikely .
From page 58 and the equally badly drawn circuit diagram you will see there are 4 paths for the magneto to be grounded ( turned off )
From No 2 in the impossible to read box in the top right corner you will see the magneto kill wire runs down to a connector and from there goes to the M terminal on the key switch so you can turn the mower off, same as for electric PTO
Second kill path is from the magneto through the parking brake switch when the brake is off then through the seat switch to ground . Also the same as before so if the brake is on then the sea switch is not in the magneto circuit .
Third path bypasses the brake switch passes through the PTO switch then through the seat switch to ground . So to kill the magneto both the seat switch ( on a different set contacts ) and the PTO switch have to be bad .
The fourth kill path is from the magneto through the PTO switch then via the MIR ( Mow in reverse ) module to ground if the reverse switch is connected to ground.
Now according to the garbage wiring diagram the seat switch is a double pole Normally Closed switch with no bridge .
If this is correct then you can verify the functioning of the switch by simply unplugging it .
Seat switches very rarely ever give you any problems .
In the 7 years I have been repairing mowers I have probably replaced 2 of them and one at least was because the plastic was broken not because the switch was bad.
OTOH I have replaced about 30 or so brake switches and a similar number of manual PTO switches.
I have never had an electric PTO switch cause a no start situation but have replaced about 5 or so where the PTO connections had burned out.
My best guess would be water in the float bowl.
I would have mentioned this earlier but needed to check the wiring diagrams first
The second best guess would be the wire to the fuel solenoid is disconnected as hosing the mower can cause the plug to fall out.
So start by taking the float bowl off and checking for water
While the bowl is off, check that the fuel solenoid plunger is retracting when you turn the key to the on position.
If it has only one wire then ground the solenoid ( or float bowl )to the engine some where.
If it has 2 wires, one should be the ground connection.
The garbage circuit diagram does not show the carb solenoid, just a connection for it at the engine plug.
Most Biggs engines ground the solenoid plug to a screw in the lower cylinder cover but a lot of Kohlers ground through the carb body.
Let us know how you go.