Think you testing has shown
as loads
voltmeter & amplifier board work ok
and
buck/boost module LED driver by it's self is a problem.
Now the buck/boost uses on/off switching to save power which can create high current/ no current load to your BMS.
I have some 1000 and 2400 Mf electrolytic caps lying around.
Now no electronic part is simple, your two cap's have a internal series resistor and it's value is listed as ESR.
Rerouter suggested adding a 0.33 ohm series resistor to the cap. One thing this does is when the cap is discharged, change from 0 volts is less with that 0.33 ohm resistor.
Remember that nothing is simple, wire has resistance and has some inductance and could have some capacitance.
You place the parts to get the most advantage using what is there.
Your BMS will not like huge loads or huge current pulses
Your buck/boost needs huge currents pulses.
Placing the Cap closer to buck/boost is a small change to the better.
Shorter and larger conductor from cap to buck/boost is another easy change(lower resistance & inductance).
Smaller and longer conductor from cap to BMS is adding resistance to this connection(more resistance & inductance) .
Now think of what a capacitor is. A simple two conductors separated by an insinuator..
An inductor is a coil of wire where you have the magnetic field of one coil effecting another.
Remember that resistors turn power into heat.
So to reduce and smooth the BMS load from the buck/boost some inductance & resistance is good.
Would be easy for you to make an air core inductor by just putting a coil in the wire connecting the BMS to buck/boost.
It is always good to do what is easy first.
C