The output ripple is exaggerated by the probing technique, but it is still strong and odd, that there is not just the regular ripple, but some extra strong pulse at a rather low rate. This looks a little like a superimposed burst mode or some extra pulses added to the set point signal of the switched mode supply.
So there is chance that the really bad strong pulses could be avoided, possibly with filtering the control signal from the front board to the power board. I would not be surprised if they use PWM plus filtering instead of high resolution DACs.
STM32F103RCT6 has two 12-bit DACs, but thats not quite enough for the set resolution (14mV/1.5mA vs 10mV/1mA), so they may be using the PWM outputs as you say.
The other parts I see:
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RC04V FRAM U6
- Winbond flash memory U8
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GS8332 350kHz single supply opamp U12
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XL7015 buck, fixed frequency 150kHz so noise shouldn't be related to that.
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AOD2810 FET (dpak not heatsinked)
Most of the pulses are at 100kHz repetition, surely this is the fixed switching frequency of the TL594 right?
As Dave stated, filtering the FET gate drive with a ferrite or resistor is probably going to be beneficial here. The ringing of the pulse is ~10MHz.
I do see some 1kHz and 240kHz spaced pulses as well, which will be something else.
edit: gate of PFET goes to via to top then R34 (10R resistor) so thats already a fair bit of gate resistance. TL594 switching frequency is 64kHz with no load.
edit2: slightly improvement with 600R@100MHz bead but not massive, might need another approach or a lower frequency material. Gate capacitance = 4nF = ~4MHz RC?