if my opponent uses turn to dust on shady spectacles attached to a sprite does the sprite die in that same beginning phase or the next from temporary?

No — Turn to Dust never makes the sprite die; it only kills the attached gear. Turn to Dust grants [Temporary] to Shady Spectacles itself, and because granted keywords stay active on attached gear (only its printed text goes inactive), the Spectacles is killed at the start of its controller's next Beginning Phase, before scoring.

The sprite dies at the start of that same next Beginning Phase — but from its own [Temporary], not from Turn to Dust. Sprite tokens print [Temporary], and [Temporary] is a status rather than a copyable trait, so Shady Spectacles' copy effect doesn't strip it away (FAQ #12414).

So both events land in the same Beginning Phase: the sprite dies to its own [Temporary], the Spectacles dies to the granted [Temporary], and the copy effect ends when the gear leaves.