I want to expand my lens collection with something more suited for portraiture.
A portrait is essentially any photo with a person as the primary subject. There is no particular lens suitable for portraits.
However I get the impression your problem is not going to be solved by lens purchases. Why ?
Currently, my longest lens is SEL55F18Z, which is just great, but some level of distortion kicks in when I shoot close-ups.
What kind of distortion ? Perspective - as you get closer to a subject, there will be a distortion due to perspective effects. You deal with this by getting further away, but that's not the only solution, as you can use software to reduce the impact of the distortion. Also sometimes distortion of this kind is useful.
But maybe you mean optical distortion by the lens itself. This is generally easily dealt with by lens correction software in photo processing applications. A new lens won't be needed here.
I have researched the topic a little bit and I'm thinking about two options (both used, and possible to get in reasonable price):
Zeiss Planar 85 1.4,
Zeiss Makro Planar 100 2.0.
Remember that longer focal lengths require more distance to use.
My questions are:
will Makro Planar be well suited for portraits? I want to shoot full-body and close-ups as well.
"Close-ups" are going to create distortions due to perspective effects. Some parts of the person or people will be significantly closer than others and this leads to an inevitable distortion where e.g. noses seem larger than they should, heads seem too large for the torsos they belong to and so on.
The "cure" here is to either accept the fact of the distortion and incorporate it into the image intentionally (compose to include the distortion and use it) or to get further away (don't do a close-up).
"Full body" - you should already be able to shoot full body portraits, but if you want a longer focal length to try and avoid some distortions, note that this will also require more distance between you and the subject. There's no free lunch here.
Keep in mind that the 50mm focal length on full frame has been used to shoot countless numbers of portraits over the decades and worked fine.
will Makro Planar produce Zeiss 3D pop like 85 1.4 does ? I'm asking because it's pretty easy to find portraits taken with 85 - but you cannot say that about 100.
That's got nothing to do with "pop" (which has nothing to do with the lens) but because 85mm is another focal length traditionally used on full frame for certain types of portrait shot. "pop" is about your ability to photograph effectively and sometimes about your ability to post process effectively (or to use the increasingly common and irritating "technique" of just ramping up contrast and saturation in post processing - yuch).
The 100mm is getting a little too long for the majority of portraits uses, but you find that 90mm, 105mm and 135mm have all been used for portraiture on full frame (and even crop frame) over the years. I've shot portraits using every focal length between 28mm and 300mm - there's no single right answer here, although the extremely long or wide focal lengths make it harder to get a good shot sometimes.
Also note that the size of lenses can be intimidating to some subjects. Sometimes a smaller lens and camera is better than a large lens and camera. These things can be surprisingly important.