Yes, there’s no free round-trip on energy...something about the Second Law of Thermodynamics if I recall correctly. ;>) But regenerative braking DOES capture a lot of the kinetic energy that otherwise would be converted to heat in the brakes. That’s how EVs get such high “mileage” claims.
Never driven a Tesla, but that would certainly change the way you drive. That sounds like race car driving — you are either accelerating or decelerating, there is no coasting.
With a gas engine, I watch stop lights WAY ahead of me and start coasting up to them way in advance. There is a little compression braking, but not much. I try to time it so I can never come to a full stop if possible.
This is really helpful for passenger comfort rather than going full speed to the stoplight, slamming on the brakes, waiting and then jack rabbit start. It also helps fuel economy.