I think you did good so far.
Putting in your electrical loads into the Electrical Toolbox can seem like a difficult process the first time you do it, but if you spend the time to examine all your electrical devices, it can be a very valuable thing to do. It should give you a simple answer. Scroll down to Copper Results, it should tell you the size service you require in amps.
You have a pretty "busy" electric panel, so your house may be bigger than 3500 s.f. or have other things like a pool (with pool pump or electric pool heater) or a hot tub, or whatever, but I have found that most people way overestimate the size of the electrical service they need. Then there are a few people underestimate the size of the service they need and have an overloaded service, but these are usually 100 amp services.
Running the toolbox for a 3500 s.f. house, with 2 4500 watt electric water heaters, 3 typical central air conditioners, 30,000 watts of electric heat, all the typical kitchen appliances with electric range, washer, electric dryer, and 1 48 amp EV charging circuit, still only requires a 200 amp service. The end result (scroll down to see this) was a Total Service Demand Load of 43,888 volt amps or 183 amps....therefore a 200 amp service.
One thing you can do is to schedule the car to charge late at night. In the Tesla app you can either tell it to start charging at a certain time, e.g. midnight, or tell it to be ready at a certain time, e.g. 8 AM. This may put less stress on your electrical system by charging when you are probably not using a lot of appliances, and will also be kind to the electric grid by chaging during off peak times. Even though I do not have time of day rates where I live, I do this because it makes sense to me to put as little stress on the grid as possible.
Even if you have two EVs, unless you max out your car's range capability daily, you can charge them every other day. Unless I know I am going to do a lot of driving the next day, I usually do not charge my MX unless it is below 50% so I only charge it every 3 or 4 days. Of course, your situation could be much more demanding.
One question: You said you used 6/2 wire and used conduit in your garage. Does this mean you did not use conduit elsewhere? If you used 6/2 THHN/THWN wire (individual wires) they need to be in conduit the entire run. Or you could have used MC cable, say in your basement, and then transitioned to conduit in your garage using a suitable junction box and hopefully split bolts or Polaris connectors to join the wires in the junction box. But if you used romex cable anywhere as part of the circuit, that is only suitable for a 50 amp breaker and 40 amp charging. If you can, post some photos of your installation.
Good luck! Let us know how it goes.