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You can get a voltage sensor that is accurate to three decimal points for literal cents, so yes, your phone does know how much energy is left in the battery. It also has current sensors, so knows how much energy is being used.
It does not know the capacity loss of the cell over time. That is why you should let the battery go completely dead and then charge it to max capacity as this will recalibrate the coulomb meter on the battery manager - batman
My understanding is that happens constantly as the battery is charged and discharged.
It tries but the value is floating until it actually has a full charge cycle. There is no way to know what the entire voltage range is. You're getting into how efficient the chemistry is over time and that is impossible to measure. It can be estimated, but that is all theoretical and not real. When the battery is fully discharged, the time, temperature, and current can be used to determine Coulombs and that is the actual energy capacity.
I'm not an expert, but I have built many circuits. My main experience here is in reverse engineering some gaming hardware that had an advanced battery management chip from Diode Semiconductors. That had such a Coulomb battery meter. The board was a 3 layer PCB and I took that as a challenge. The batman chip was also a small ball grid array (pins are inaccessible on the back side. I didn't have xrays when I did the first trace of all pins, so I had to fully understand the chip to trace all connections only using the vias. I think I have a chip or two in parts drawers that do the same thing, but I never built anything with them, or at least haven't yet.