Question

What does it mean for a compound to become its "stable form" when it transitions? Is this related to equilibrium?

Answer 1

The stable form of a compound simply means it can stay at this form in natural conditions like normal temp (room temp) and normal pressure and other general parameters.

For example the more reactive metals like sodium are not stable on their own but it can form a compound by bonding with another element such that it becomes stable.

Sodium on its own is not stable but its compound (NaCl) is stable form

As your question the stable form of compound is not related to the equilibrium.