Does the winding move if current is applied to the solenoid?
It is known that a current winding can draw a metal bar into the winding. Will the winding itself contract at the same time?
Ideally, it will not, but what current? Permanent or variable? In practice, conductors move under the influence of current, or rather Ampere force. Therefore, the coils of starters and relays always buzz when powered by a changeover. Read more in this article - https://electro.tomathouse.com/en/zakon-ampera-prostym-yazykom.html, and draw conclusions about what will happen to the coil.
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