The electrician said your panel was "overfull"?? Sorry, but I call bullshit on that. If your panel was overfull you'd be blowing circuits every day. Besides which, what does "overfull" even mean? What, you have breakers waiting in line to get a slot, just hanging out of the panel waiting until one of the other breakers leaves, like an "overfull" restaurant?
Before you decide whether or not to get a Tesla, find yourself another electrician, because this guy saw you coming. In 2015 we bought a Nissan Leaf in California and I hired an electrician to install a charging unit. When she (yes, she) opened our electric panel it turned out it was an old GE Zinsco panel which, by law in CA, could not be altered in any way because of a history of failures causing fires. The only way she could install the charger was to replace the entire panel, which I had her do. Total cost for new panel AND running the line clear to the other end of the house where the garage was located: $1500.
On top of which --- and I sincerely apologize if this offends any electricians out there in Tesla land --- one of the scams a less than ethical electrician will run on an unsuspecting customer is the "your panel is full, you can't add anything, we need to put in a new panel." 9 times out of 10, this is pure bullshit. How do I know this? We have a house this entirely electric, no gas service of any kind, everything is electric. Since we moved in I've had an entire solar panel system installed, replaced a water heater, added a charger for our electric vehicles, and am now looking at installing a mini-split system. I've had 1 electrician tell me none of this could be done without replacing and/or adding a sub panel. The real electrician I ended up hiring just smiled and shook his head... then he doubled up most of 10 and 20 amp breakers, and installed everything. House is still standing.
If you have a 200 amp panel remember this: Even if you turned on every appliance and every light in the house, everything that draws electrical power, you still wouldn't be pulling 200 amps, because of the aforementioned elsewhere in this thread, the 125% rule. Do you have every appliance and every light turned on at the same time, ever? Of course not. I'd even wager half your major appliances (heat, water heater, dryer, stove?) are gas, not electric.
Get another electrician, one who understands how to calculate the power load your panel can handle against the power draw your house pulls at full capacity. Then pay him what will be a reasonable charge to install your charger, and buy your Tesla.