Ground plane under power inductor in DC to DC converters
Let's look at an example of a design implementation of a non isolated DCDC converter, I choose the LMR36015 from TI. This is a 60 V, 1.5 A buck converter for automotive applications.

On page 36 there's a picture of the PCB layout, I converted it to grayscale except the area containing the inductor:



Note how the area is fully covered in copper except for two gaps to separate the VOUT, GND and the switching node.

Note that here a shielded inductor is used. That's nothing fancy,nearly all modern switched converters use shielded inductors. Some use toroidal inductors but these also keep the magnetic field "inside" so it should be OK to place a (ground) plane below such an inductor as well.

For an isolated converter you need a transformer, without it isolation cannot be achieved. There the same applies as mentioned above, as long as the magnetic field remains inside the transformer, a copper plane should not affect it.

However there are other concerns regarding the isolation. The transformer is the device which forms the actual isolation. So in almost all isolated switched converter designs I have seen there is no copper plane under the transformer, instead there is always a copper free space and/or a slot in the PCB in order to make sure there is no leakage between primary and secondary windings of the transformer.

Here's an example of an isolated DCDC converter (SMPS), again the coloured part is the transformer.

 

Note the large spacing between the traces connecting to the left (primary) and right (secondary) sides of the PCB.

Optionally part of the PCB could be drilled out along the thick line running from top to bottom right through the transformer.