@JohnH01 Those Conti DWS06+ in 245/35R20 XL should work, and would be a very good choice for you I think. The XL load rating is important for this car, and the model you linked to has it.
The 245/35R20 size is good, it will fit
better on the 20x9" Uberturbine wheels than the stock 235/35R20 size which is literally stretched (I've no idea why Tesla chose such a fitment).
The Conti DWS series is known for being better in the snow than most UHP allseasons (the "S" in the "Dry Wet Snow" name). The tradeoff is it's not the sportiest UHP allseason in the dry, but it does perform well year round. If you want to run one tire year round in Chicago I think it's a great choice.
Personally, if I lived in Chicago, I would go with
@oreobbq's suggestion of separate (smaller) wheels with true winter tires (either Performance Winter or Studless Ice & Snow, depending on preferences). But that's because I'm an aggressive driver, I push my car pretty hard through the twisties often, so I really like running true summer performance tires (<= 300 TW) in the warmer seasons. You might not feel the same need for dedicated summer rubber, and that's totally fine.
I should note I haven't used any Conti DWS series on my own cars, but I have experienced them on friends cars, and read quite a number of reviews of them over the years, so I'm reasonably confident in this assessment of them.