[oil pan 4]

I was able to use a 12 amp evse and small apartment dryer together just fine.

I used a 16 amp evse and full sized dryer together just to see what would happen. The breaker buzzed and the dryer cord got warm. It was drawing 38 amps on a 30 amp circuit. Don't do that. I did it so you don't have to.

According to national electric code clothes dryer circuits are specifically listed. They are to be a dedicated circuit, which means only 1 receptacle is allowed to be on the circuit and only one thing ran off it at a time.
The continuous load is not to exceed 24 amps.
So even if you run 2 things off your dryer circuit and those 2 things only draw 24 amps when ran together, you still can't do it.
You can unplug the dryer and plug in an evse that does not exceed 24 amps. If you plug in a 32 amp charger, nope not a good idea. If you run that 32 amp charger on a 30 amp circuit for a few hours that 10 gauge wire will get pretty warm.

For my 16 amp evse I have a 12 gauge wire circuit on a 20 amp breaker.
For anything bigger I have my 125 amp welding circuit on 4 gauge, say if I find a 20kw home chademo.