This is all to do with the suspension/steering geometry and wide low profile tyres of a type used 'out of season'.
My RC does this on full lock but only in the colder months as the tyres are really summer spec. Mercedes had a real issue with the same problem on it's 'all-wheel drive' models. They 'cured' it by offering winter tyres to customers who complain about the crabbing ..
The AMG went a few years back. Now driving my RC on the factory fitted Dunlop Sport Max. Very competent tyre, quiet and grippy in the wet.
If I manage to wear these out during my ownership I will probably go back to Michelin, with the Pilot Sport4S
I tried Pirelli tyres on my AMG and they were an absolute nightmare! Slightest bit of damp and I might as well have been driving on ice. No grip at all
The Michelins I replaced them with were like night and day. Phenomenal grip in all weathers/ Plus I nearly got 12k miles from the rears before replacing them at 3mm tread depth.
One can certainly leave the 12v battery connected to a trickle charger, such as the CTEK.. One can also use the traction battery to maintain the 12v battery as Lexus recommends.
See attached document
Maintainace of hybrid battery.pdf