Michael, no doubt, by definition, cold spring is an "intentional deformation" but in back of the definition was the fact the cold spring was supposed to be made by "cutting short" or "cutting long". In this case, the intentional deformation is rather an intentional strain.

In an old Intergraph/Coade training document there is a nice definition:
"Cold Load (CL) is the intentionally incorrect load at which the spring is pre-set, in order to get to the Hot Load after moving."

What you essentially said is that that applying a force (load) in a piping system results in deformation of system and must obey to rules of "cold spring".
It is your interpretation and maybe is in harmony with the definition, but I do not second your opinion. On the same logic, applying forces on a beam simply sustained will get "deformation" of the beam, however nobody defines this fact as "cold spring".

You may have in practice spring supports with SUS displacement as a quarter of inch. One contractor may consider 0.25" is within construction tolerances or as you said "manufacturer imprecision".

In the end, nothing wrong to consider such deflection under CL as "cold spring"- just curious you tell Caesar there is a "cold spring"?

I remain on my opinion: a spring support is a force in system.