Electronic – This op-amp buffer is oscillating and I can’t figure out why

There are different models for the LM358 unit. PSpice simulations based on "LM358" result in a phase margin of app. 50...60 deg. But apparently, this is a very simple model.

However, when using the LM358/NS model the margin is slightly negative! This explains the observed instability during measurements. Hence, external stabilization of the feedback scheme is necessary.

Compensation: A compensation scheme (series connection R=500...1000 Ohms and C=50...100nF) at the opamp output node provides a phase margin of app. 50 deg. (simulation).

Your third image is not a (source) follower, rather it is a common-source amplifier and generally is configured to provide gain > 1.

A source follower looks like this:

Note that there is no drain resistor at the top and that the output is taken from the source terminal rather than the drain.

\$V_{out}\$ will follow \$V_{in}\$ with a drop of roughly the gate threshold voltage of the MOSFET, \$V_{th}\$. This may be somewhere around 5V depending on the device, so one might reasonable choose a BJT emitter follower instead:

You can see the circuit is essentially identical excepting the transistor type. \$V_{out}\$ will follow \$V_{in}\$ with a drop of \$V_{BE}\$, typically only 0.7 V.

The input impedance of an emitter follower is relatively high, and it's output impedance is relatively low. So placed between a resistive voltage divider and the rest of the circuit (such as an amplifier input) has the effect of stabilizing the bias voltage developed across the divider against variation due to changes in current drawn from the divider.