What to use to flatten and prep wall before installing Schluter Kerdi membrane for tiling?

I am remodeling a bathroom that was originally done with 1/2 inch drywall. I opened-up the walls to move plumbing and electrical as required and then covered-up those sections with new 1/2 inch drywall.

The shower and tub areas are going to have tile on the walls as well as the entire bathroom floor. I've already done Ditra + tile in other rooms so no questions there.

Here's my problem: Whoever built this room put on a skim coat that is, by the looks of it, about 1/8 of an inch thick in some areas. So my new drywall is 1/8 thinner than the existing wall in some sections and a perfect match in others.

Now I have the problem of matching all of this up before installing the Kerdi membrane.

What type of mud do I use for this? Is a general purpose compound good? Remember that I will have to apply unmodified thinset over it in certain areas in order to adhere the Kerdi membrane.

I don't think I can skim coat with thinset. I'm not good enough to achieve a smooth finish and it can't be sanded. My best guess is that the solution is to skim coat the entire room, tape corners as needed and then thinset where the Kerdi membrane is applied.

Is a 1/8 skim coat strong enough to support the tiles? I have no clue how well these layers will bond to each other.

Can I use a premixed mud compound or do I have to use a setting-type material?

Just to make sure I have the process straight: First you skim coat the entire bathroom and then you go back and tape conventionally. Correct? Or is it the other way around?

I've done a bunch of tape-and-mud-ing and even fixing very large (2 foot) holes in other rooms. I am generally comfortable with that aspect. I just haven't skim-coated an entire room and much less applied tile on top of it.