Finally sized up from my 16A unit and the difference caught me off guard

Pretty normal for them to want a load calculation before adding a 40A circuit. I have a 100 amp panel and two EVs on it. I swapped the old water heater for a hybrid and went to a heat pump A/C before I put the charger in, so I had the headroom. If your panel is already close to full, that's what they're checking for.

Mine went the other way. The panel itself was fine, but it was on the wrong end of the house from where the car parks, so the run had to go across the basement and through finished ceiling. Total for the 14-50 came to $3600, which was a lot more than I'd budgeted for a "just add an outlet" job. One thing I'd say: the 'portable' label doesn't mean much to an electrician. A 32A unit plugged into a receptacle is a 40A continuous load as far as code is concerned, so it gets treated the same as a wall-mounted one. If it's going to stay plugged in at home anyway, ask whether hardwiring is an option. You lose the receptacle as a failure point, and in most places you don't need the expensive GFCI breaker either.

Mine's hardwired outside and the electrician didn't ask about the panel at all. 200 amp service though, and in Texas almost everything in the house is already electric so I guess they figured it was sized for it.