Slip control stays on? Or transmission?

Could be several things.
Probably associated with the ABS/traction control.
Have you turned it completely OFF for a while and tried again ??

 

How old is your 12V auxiliary battery?

 

tires, speed sensor, wiring, ecu, inverter pump, icm module, time to read the codes

 

There is no way that a "normal" human being can tell if the 12 V battery really is "nice and strong" in a hybrid vehicle just by look and feel.
A meter is needed to test.

 

If you have a way to get the trouble codes (which are there, because dash lights are on), that's the quickest way to what the car wants to tell you. Codes from the braking and traction systems can be read (in abridged form) with a short wire and some blinking-light counting, if no scan tool is available, but that won't retrieve codes from all possible subsystems.

It's possible for the gas on the wet road to be directly related, indirectly related, or not related to what you're seeing now; coincidences do happen. The codes will be most informative.

Because the car was in READY at the time, the voltage on the 12 volt bus was coming from the DC/DC converter just then, irrespective of the 12 volt battery condition.

 

While it is true that the car runs on inverter power once it boots into READY mode, my experience is that starting it on a flat 12V (or a flat traction battery) leaves a legacy of fault indications and dash lights.