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Available capacity with 125amp breaker at home

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Attached are the photos of my circuit breaker. I do have a 30amp dryer which you can see by the tandem circuit.
View attachment 243390

View attachment 243391
Odd to see a 30A 240V breaker (not a tandem, BTW. The one at lower right is a tandem; two breakers occupying one space.) labeled washer and dryer. That would leave a 120V 15A duplex outlet protected by one side of a 30A 240V breaker.

Are you using an electric clothes dryer? If not, and if its outlet is near the garage, you could easily have that circuit extended to a Nema 14-30 outlet in the garage, enabling you to charge at 17 to 18 miles per hour. That would be much less labor and materials cost than adding a 50A breaker and circuit to the main panel.

I use a 30A dryer outlet that was already in my garage to charge overnight during super-off-peak rates (10pm to 8am).
 
Odd to see a 30A 240V breaker (not a tandem, BTW. The one at lower right is a tandem; two breakers occupying one space.) labeled washer and dryer. That would leave a 120V 15A duplex outlet protected by one side of a 30A 240V breaker.
Your assumptions were different than mine with that labeling. My assumption was that it was a space saver all-in-one combination unit that runs from a 14-30 outlet. Or, don't overthink it--the labeling may be unclear. The dryer is on the 14-30, and the washer can just run from any 5-15 outlet in any room. It doesn't have to be specifically labeled in the breaker panel.