Are there active electronics in basic Powered Up motors? Powered Up is a more advanced system than the Power Functions system that it is replacing. Does each component contain active electronics that identify it to the hub that it is connected to?
No.

Powered Up does provide the ability to send data between hubs and connected modules via the addition of two additional wires not present in the 4-wire Power Functions system. However, the system appears to be able to operate basic components using only analog control just like Power Functions. For example, here's a look at the internals of the new train motor from Eurobricks:



There are only two components on the board. C2 is a small capacitor in parallel with the motor to address back EMF, and the larger component in the middle is a fuse to prevent damage to the motor or other components when stalled.

You can see in the photo that the two new PU wires (5 and 6, labeled  ID1 and ID2) are connected directly to VCC and GND respectively. It would appear that if these connections for ID1 and ID2 are detected by the hub, the component is treated much like a PF component and M1 and M2 are used to control it. Digital electronics are not required.