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.