Technically yeah they are literally a tiny weight on springs. But they are in a tiny silicon package that is effectively "solid state"
Its operation fundamentally involves (near infinitesimal) movements, but then so does a cell phone pole. I don't see what we gain with debating its "solid stateness" (especially when hedged with "effectively"). Maybe you could point to some effect that this distinction implies?
To me, moving parts generally refers to physically coupled but distinct pieces that move relative to one another. Otherwise heating anything that contained a piece of metal by a few degrees would disqualify it.
More importantly, https://en.wikipedia.org/wiki/Solid-state_electronics:
”The term "solid state" became popular in the beginning of the semiconductor era in the 1960s to distinguish this new technology based on the transistor, in which the electronic action of devices occurred in a solid state, from previous electronic equipment that used vacuum tubes, in which the electronic action occurred in a gaseous state.”
⇒ the term doesn’t reference the hardware being solid.
Wikipedia:
> The term is also used for devices in which semiconductor electronics which have no moving parts replace devices with moving parts, such as the solid-state relay in which transistor switches are used in place of a moving-arm electromechanical relay, or the solid-state drive (SSD) a type of semiconductor memory used in computers to replace hard disk drives, which store data on a rotating disk.[6]
In short: neither the term definition nor usage is entirely consistent.