I can not look up the exact spec but can point you in the right direction.
I shall use this diagram from Jacks as a refference
https://www.jackssmallengines.com/jacks-parts-lookup/manufacturer/kohler/oem-cross-reference/exmark-mfg/ch23-76569-exmark-mfg-23-hp-17-2-kw/ignition-electrical-5-24-372-ch18-750
Locate the regulator , part # 39 on the side of the blower housing.
There should be a flat strap, part # 37 bridging the engine ( ground ) to the outside of the regulator making the ground contact for it.
This strap regularly breaks so the rectifier is not grounded & can not recharge the battery.
When I repair them, I make some new wires with eye terminals to go between a blower housing screw & the rectifier ( one each side to a different screw ) .
Once you have located the rectifier measure the voltage from the purple wire to ground and to the battery negative , engine off & engine running full speed.
Also measure the same points for AC voltage. If you get an AC reading then the rectifier is toast & needs replacing.
Also measure the AC voltage between the two white or yellow wires to ground and between each other.
The ground readings should be the same and the reading between the two should be between 28 V & 36 V AC that will end up being 13 to 14 V DC by the time the mower sees it.
If these don't happen then the alternator is cactus
At this point stop, remove the blower housing and remove the flywheel, check that the magnets are all there & not fallen off.
Assuming the previous is not the case & the alternator is good, then measure the voltage Purple to battery negative and between the battery terminals, engine running full speed.
If these are different then the purple wire has broken somewhere so the volts are not getting back to the battery.
Post your results.
After that then clutch is the next culprit , but like learning to walk, one step at a time.