Both ac machines and dc machines can be used as motors or generators under the right conditions.

An alternator is basically a permanent magnet AC generator with a diode bridge at the output, so power only flows OUT of its terminals. That’s why it won’t motor.

A regular squirrel cage induction motor can be used as a generator, if there is an external ac source to provide the necessary excitation, and the external prime mover rotates faster than synchronous speed. Big wind turbines commonly use this approach.

To do what you want for automotive applications, you need a power electronic converter that can adjust the voltages on the fly to direct power either into the machine (as a motor), or out of the machine (as a generator). Note that this is very different from just changing the polarity between battery and motor.
If you only switch the applied polarity, the motor just tries to quickly change to spinning in the opposite direction. This works for braking, but puts a LOT of heat into the motor. Power is still flowing from battery to motor, and no re-generation occurs.