Liquid Amps

What's even more important than the type of distortion is where is the distortion located. Our ears hardly care or notice distortion in the bass regions relative to others. Most subs have horrendous distortion and are driven by cheap digital amps. Thus, it's not only the type of distortion that matters, but where the distortion is present too.  

+1 the problem area is seen in the Fletcher Muson curves; our hearing is tuned to be most sensitive at birdsong frequencies, 3-7KHz, where a lot of harmonics of instruments show up, and thus also harmonics generated by the audio chain.

Essentially, this is why tubes are still around- tube amps generally speaking tend to make less distortion that falls into this region.

All this being said...I don’t think the BIGGEST problem with systems not sounding "liquid" is the fault of higher order distortion in SS amps. I don’t think Atmasphere made the claim that it’s the "biggest" problem either, so we may not even disagree per se. I just want to point out that IME the biggest problem with systems not sounding "liquid" rests with the speakers and source first...not the amp.

If the speaker is more revealing, it will totally play the distortion that makes many solid state amps sound bright and harsh.
This distortion is not a lot as far as test instruments are concerned, but to our ears it is, which is why its so easily heard (and why tubes and tube amps are still around decades on after being declared ’obsolete’; if they were really obsolete they would have ceased production long ago).

The real problem we are dealing with is that the audio industry (like many other industries) does not like to deal with inconvenient truths. In this case it is the fact that our ears, while seemingly inaccurate and insensitive to so may aspects of audio, are more sensitive than the best test equipment when it comes to detecting higher ordered harmonics.
BTW this is extremely easy to prove with very simple test equipment!
Anyway, IMO the industry should put a ’weighting’ (like we do on noise) on harmonic distortion. Less weighting on lower orders, higher weighting on higher orders (particularly the 7th) so when you look at a spec sheet, you can finally tell what the amp will sound like! Right now, the spec sheet has marginal usefulness (unless you keep a bird or hamster) since it really doesn’t tell you how the amp sounds. And ’liquidness’ is all about how the amp sounds.
Some solid state designers get this- notably John Curl and Nelson Pass. Both will freely acknowledge that tubes still rule the roost as far as liquid or smooth sound is concerned. I think Nelson has done more work in this area, and the amp I mentioned is easily the smoothest solid state amp made.
BTW I think the McCormick is a very good amp too, but the little VFET amp Nelson came up with totally smokes it in the smoothness/liquid category, without sacrificing detail in any way. Of course, tubes do that too :)

What is the most “liquid” sounding solid state amp and is “liquid” even a thing?

It is, and its a description of how the amplifier makes distortion, or more to the point, what distortions it **doesn't** make.
Solid state amps have a long standing reputation for sounding brighter and harsher than the actual music, this despite having typically very low distortion overall.
The problem is that the distortion they *do* have is entirely that of types to which the ear is keenly sensitive, moreso in most cases then excellent test equipment. This is because the distortions in question are higher ordered harmonics (5th and above) which the human ear uses to sense sound pressure. You probably don't have to imagine how important it is to be able to tell how loud a sound is! Amounts of 0.005% are thus audible.

For this reason, and also due to the distribution of harmonic structure in musical instruments (which is not a coincidence), the tiny amount of distortion most solid state amps make is actually really audible, hence your opening question!
Some of this is caused by non-linearities in the solid state devices, and some is caused by the application of loop negative feedback, which is used to suppress the distortion of the former. Its a bit of a carrot on a stick: no matter how much feedback is applied, the actual use of feedback will generate its own higher ordered harmonics.
This fact has been known for at least the last 65 years (for those interested, see the writings of Norman Crowhurst)!
Generally speaking, tube amplifiers don't make as many of the higher ordered harmonics and so sound smoother as a result.
But in the late 1970s, Sony developed a new kind of power transistor called a Static Induction Transistor (SIT), also known as a VFET. This transistor had linearity similar to a triode power tube and even had soft clipping characteristics. Unfortunately, Sony, like they were with so many of their innovations, was very precious about the use of their technology, and the only amps built for quite some time were their own VFET amps, which were not particularly reliable. They went by the wayside.
However Nelson Pass took an interest in the device and even had some made at one point, although the semiconductor house that made the SITs for him later went out of business. Because of the rarity of the devices, Nelson never made a production amplifier with them, but he did make a kit, and by all accounts it is easily the amplifier you are looking for- it has the least 'transistor' artifact of any solid state amp I've heard.
The amps don't make a lot of power (about 20 watts), and the kit is not being offered to the best of my knowledge, but you might be able to find one that didn't get assembled that is for sale. It would not be that hard to find someone to build it.