Each supply is used to shift levels by increasing the output swing at each stage from Vdd to Vcc to Vbat. There are other functions besides level shifters. The Boost voltage is generated from the LO side PWM to create another level shift from Vdd and PWM LO side to V-Boost.
The HO, LO drivers are about 7.5 Ohms, which you can tell from their short circuit current of 2A with Vcc=15 which also increases the gate voltage to achieve that internal RdsOn.
So as well as voltage boosting level shifters, each stage also reduces driver Resistance from about 1Megohm input impedance to 7.5 Ohms driver with at least 3 internal shifter stages to external RdsOn output impedance.
But you have a long way to go to understand how MPPT PhotVoltaic (PV) to battery charger works.
The switched load must consider the ideal Inductor value for frequency, impedance, and current losses. The average MPPT load on the PV AC impedance at the PWM rate must match the DC impedance Z=V/I even though the PV is a current source.
Consider matching the PV source impedance Vmp/Imp=Zmp if operating in CCM mode.
Although you may have a low ESR big cap across the PV, it is a high impedance current source at DC but almost a short circuit at step pulse rise times so the switched inductor creates the series load impedance (Z=2pif*L) at the fundamental. This is an approximation as the pulses to PV caps are integrated.
Often this MPPT is done in 2 independent stages PV to Vmpt with matched impedance Zmin when there is demand, otherwise, it is higher impedance. The 2nd stage DC-DC converter then draws the load limited by the MPT to charge the battery for it's CC, CV requirements. You can do it in 1 stage, but this demands control of both input Z and output Vbat current at the same time... all the while, Solar current can change with a cloud.
I suggest you learn more about commercial MPPT controllers by studying their designs.
Here is a simple MPPT design that uses 28V battery with an iron core transformer coil for you to study.