The capacitors are simply decoupling, just rather more is needed for a high-current
motor controller.
A three-phase MOSFET bridge is used to drive BLDCs. The power electronics issues
are mainly those of getting the protection circuitry right so you don't blow-up MOSFETs
(yes, they explode if you get it wrong - eye-protection is needed).
At a minimum you need a proper MOSFET high-low drivers, overvolt protection on
the gate-source side, transient spike suppression on the main power bus, attention
to low-inductance signal routing, and most importantly rapid over-current shutdown.
With 48V at dozens of amps every part of the circuit is subject to intense noise pick-up
if you get the layout wrong.
Its a big project, you'll need to do your research and be prepared for failures,
and you will need an oscilloscope and a large bench PSU.