When you charge at home or at a public (non-Supercharger) charging station your Standard Range Model Y is limited to 32 amps. As previously stated, when you are charging using a Tesla Supercharger station the Tesla Model Y's on-board AC-to-DC converter and on-board charging equipment is bypassed. The 40 amp circuit you currently have is all that you need for using the Tesla Mobile Connector with the NEMA 14-50 power plug to charge at 240V and 32 amps (the highest charging amperage your Standard Range Model Y can draw when charging (other than when Supercharging.)
The Standard Range Model Y Supercharger session is limited as compared to the Long Range Model Y when using a Supercharger but in actual use you would not notice the difference in Supercharger charging rates (170kW maximum for the Standard Range Model Y, 250kW maximum for the Long Range Model Y.)
Reasons to consider the Tesla Wall Connector include:
Can charge at up to 48 amps (on a circuit with wiring rated for 60 amps, assumes the Tesla vehicle can charge at more than 32 amps.)
Does not use a plug/receptacle, designed to be hard wired into the circuit. When installed the Wall Connector is fully weather rated for use in all weather conditions, with no power plug and receptacle where water can get into the power connection. The Wall Connector can be installed outdoors with no weather issues.
Only requires two powered wires in addition to a ground wire (no neutral wire is required, used.) The two wire run can save some cost during installation. For example, you would have the electrician install 4/2 wire instead of 4/3 wire (if 4 gauge wire was used.)
Tesla has stated that, in the future, the Wall Connector will be able to support load sharing so that two or more Wall Connector units can be installed on a single circuit.)