When you shut the car off, one of the menu choice options is to continue to run the cabin conditioning. If selected, things will continue for about 30-minutes. Other than that, you need to either set a departure time or request immediate conditioning from the app, or set it up in the car's menu while it's still on. the radio will shut itself off, but you can just hit the button again, and it will turn back on and run for its timed cycle again.
Your old 3-series didn't have a resistance heater or electric compressor, so if it gave you any heat or cooling, it was whatever residual was there from when you last ran it.
Note, on the REx version, any heat comes from resistance heaters which can make a fair dent in your battery capacity. the BEV version has a heat pump and resistance heating as a backup, but the REx version does not. The BEV is thus more efficient. that, and the combination that the REx is heavier is the primary reason why the REx isn't as efficient as the BEV.
2011 535i x-drive GT, 2014 i3 BEV