How smart are smartphone batteries?

Is our stomach smart?

Probably not.

Then how does it know that it is full?

Our stomach sends signals to our brain that it is full with reference to the hypothalamus, blood sugar, and having food in the stomach and intestines.

Similarly, smartphone batteries are not smart. The remaining battery capacity is measured using the voltage at which it is operating (typical).

Below image gives a good idea.

In case of fast charging, the charging brick delivers the power required with reference to the battery voltage, temperature and remaining capacity.

Batteries are not smart. But the whole system consisting of battery and CPU takes smart decisions.