If the regulator is kept very close to the FPGA, the 4# 680uF could serve as the output caps for LTM4637. Usually, these capacitance is enough for normal operation of LTM4637. But for the system, how much capacitance are needed depends on the
Please check page 18 of datasheet. It list theta-JA values. All based on the actual PCB implementation using demo board. I'm not sure if we have other info that this. Please connect to local ADI sales team if you need the other data.