Electronic – High freq OP-AMP voltage follower is ringing and is unstable

One issue is that the filters to get rid of the PWM may be attenuating the signal you want to measure, so I would suggest a notch filter to get rid of much of the PWM signal.

The Fliege notch filter is a versatile and somewhat forgiving filter, and I have run one up for the 20kHz:

It has this simulated response:

The notch depth is -55dB here, although I would expect -40dB as a more realistic response with real devices and layout. The bandwidth between the -3dB points is about 2kHz.

As this filter is unity gain at DC, it would be simple to introduce a DC offset to run on single supply.

Note that R7 is only present to enable the simulation to converge, and the notch depth is proportional to the ratio \$ \frac {C_0} {R_0} \$

You could then use a high pass filter to attenuate any harmonics of the PWM drive signal which may simplify the rest of the signal chain.

I don't think you chose the wrong opamp, at least not based on what you are showing here. It looks like power supply noise to me based on the obvious correlation between supply and output. Also the noise is periodic at about 15-20ms which would match 50/60hz.

Opamps have a specification power supply rejection ratio, which says how well the opamp can isolate the output from the power supply. Looking at the datasheet for this opamp, PSRR is very good, about 140dB, but that is at DC and PSRR is frequency dependent.

Looking at your second picture, I see about 1V p-p noise on the power rail, and 20mV on the output (not 200mV - wrong probe setting?). You are seeing maybe 35dB PSRR in this configuration, from 1V to 20mV. Looking at Fig 12 in the datasheet (PSRR vs Frequency) this ratio happens around 10-100kHz. It wouldn't be surprising if you have that sort of noise on your power rail, switching converters typically run 50khz upwards.

You should probably add some filtering on both power rails to ground using L-C filters. There is no easy answer on what exactly to use and it may not be simple to do this 'properly' - this PDF has some good information. However if it were me, I would grab some power inductors and capacitors, check the cutoff frequency using the formula, and give it a try to see if it helps reduce the noise. For example I might try 22uH/47uF for 5kHz cutoff.