I had a similar experience. No trade in, paid with cash. It took a whopping 8 minutes, 5 of which was me going through my own checklist to make sure there were 0 build issues.
LOVE the Model S (2021), but people are bored with Tesla fellating, so here's the downside: I'm concerned with the front suspension. Car isn't even 2 years old, and I've had to use the warranty to replace the front suspension once (different part #s, does that mean old ones had a build issue?) because it sounded like a crazy shopping cart wheel when flooring it. Then again a year later when one of them started squeaking like a 20 year old car going over speed bumps Similar to mine:
I see similar postings from other S and some X owners.
MS has computer controlled air suspension. I cant see how it has issues like your describing unless you just got a lemon out of the factory.. My MX rides like its on air. I did have an issue early on where I got a very slight shimmy at 38mph. Turned out it was a setting on the suspension height.
The MX can adjust the body height automatically (as can the MS). The tech found something in a Tesla white paper and adjusted the base height setting and the shimmy disappeared.
Could be as simple as something like that.