I would be weary listening to others when it comes to the subjective connection between driver and car-any car.
Your beast weighs 4,250 lbs. No oversized tires, heavier sways, lighter wheels, stiffer shocks, etc. will overcome the dead weight of over 2 tons in a turn.
The M3P is a "performance sedan" whatever that means. It's an over-powered, straightline muscle car that will never beat the handling of even a first generation Cayman S (2900lbs), or an old 911 S (2300lbs). Dead weight wants to travel straight (check out some Nürburgring videos of M3Ps trying to chase even a baldy driven 911 GT3 through the turns of the Nordschleife). It's just physics. Even after Porsche applied all its skills to make the Taican (5100lbs) "handle" like a sports car, it is just too heavy to be truly nimble and agile.
I own the same car as you, and its drive-by-wire throttle and indirect steering feel, its heavy wheels, its shitty seats with no side bolsters to hold me in place when I accelerate out of a turn - all that disconnects me from the visceral experience and elation I get driving my Porsche that truly is glued to the road and keeps my body planted in place, and supremely in charge.
But teasing all that from an M3P is just asking too much, I think. Tesla pioneered a wonderful driving machine that still leads the way to the automotive future, despite all imitators to date. Let's wait for the battery weight to come down, then we can maybe expect truly sports car handling AND range.