The real question is what amperage your existing charger draws and what your home's actual demand looks like - most residential 200-amp panels can handle a second charger if the first one isn't running at maximum capacity constantly, but that depends on your other household loads and whether both cars would charge simultaneously.
Two Wall Connectors each pulling 48 amps would be tight on 200 amps total, so the electrician's assessment might be right if your household already uses a decent chunk of that capacity for HVAC, water heating, and other appliances.
Before dropping $3,500, get a second opinion from another electrician who can run a load calculation specific to your panel - they'll check your actual usage patterns and tell you whether you can get away with a breaker reconfig or truly need an upgrade.