I'm a driving enthusiastic and former track day enthusiast, so I'll throw my 2c in. Never owned a BMW but I've driven a decent number over the years, various versions of E36, E36/7, E46, E60, E90, E92, F30 including some M cars (E36, E60, E90). Oh, and an i3.
First things first, I agree there's no better daily driver so long as you can charge at home, which it sounds like you can. Fast and fun, yet quiet and relaxing - nothing does both of those together better than a good sporty EV. And waking up to a charged car every morning, never having to stop to fill up in daily driving, is priceless. Plus no worrying about carefully warming up an engine or smelling the exhaust while it's cold. And you can chill out with your baby or dog or yourself napping with the A/C on but no engine fumes. The list goes on...suffice to say, I have zero desire to ever go back to gasoline/ICE for a daily driver. A good EV is way better in that role.
Performance vs LR...look at your car history. Get the Performance, this should be an easy choice for you.
Yes the LR is surely quick enough, and yes they pull the same at highway+ speeds. But you'll probably want the P's Track Mode even if you never take it to the track. Track Mode is the only official way to dial back the nannies. If you want to put the power down coming out of turns/ramps, you need Track Mode. If you want the freedom to slide either or both ends of the car as you wish, you need Track Mode. Etc. All of its 3 major settings are useful for fast/hard driving on the street. I doubt you'll want to commute in Track Mode daily, but I think you'll be glad to have it available.
The comments about the stock suspension are on point though. It's soft and very poorly dampened from the factory. Taking freeway ramps like you're on rails? Not happening with the stock suspension. It's loose and unsettled with terrible mid-corner response. Let's not even talk about how out of control it can get trying to drive fast on twisty, bumpy, uneven back roads. But a good set of coilovers, plus front lower control arm bearings, completely transforms the handling and responsiveness. That will absolutely give you the locked in handling you want. Do those at a minimum. If you want and have budget you can also go to town upgrading all the other control arms with their accompanying bushings.
You will always feel the 4000 lbs weight, but you will also feel how low and centered and well-balanced the weight is, especially once you fix up the suspension. It's almost like a heavy but well balanced mid engine sports car. After upgrading the suspension, this thing honestly handles better than any 4 door ICE car I've ever driven.
You really don't need to lower this car btw! Stock height is probably better for handling over nasty real world roads anyways. The reason to go straight for coilovers is there aren't really any good standalone / fixed perch aftermarket dampers options for this car. All of the really good damper upgrades are coilover kits.
Side note: Apparently older Model 3's (LR or P, doesn't really matter) had stiffer suspension tuning from the factory. Not sure how much better, it's been too long since I drove one and it was a very brief casual drive. Newer ones, approximately 2021+, are quite soft though with really crappy damping.
Power drop off with low state of charge...yup it's a thing. From what I've read the new S holds power really well into lower states of charge, so it's not surprising you didn't notice this with your Plaid rental. (Plus it's starting with such an excess of power.) Hopefully that will trickle down to the 3 at some point. I don't think the 3's power loss at low SoC will be an issue for your daily driving though!