No SAE J3016 defines each level. Many states (including CA) use some SAE definitions in their regulations though.
Tesla is making clear city streets (FSDBeta) is incapable of meeting L3 or greater requirements, and the finished/wide release version will not change that.
Anything they do that us L3 or greater will be some future version that adds elements city streets simply does not and is not intended to have.
They especially call out the object and event detection and response (OEDR) sub-task as being too limited to operate beyond L2, with a list of circumstances that could cause failures because the system may not even be capable of recognizing (let alone properly responding to) them- adverse weather, complicated or adversarial vehicles in the driving path, construction zones, emergency vehicles, large uncontrolled intersections with multiple incoming ways, occlusions, road debris, static objects, and unmapped roads
As such the inherent design of the system may result in situations the human driver MUST respond to without the system being capable of alerting them to do so.... (which means it can't be L3, let alone higher).