If you prototype yourself - either an alternate timeline version of yourself for a Time player, or a Dreamself for anyone else - does the Sprite gain your class powers?

Yes, much like how Becsprite still had First Guardian powers- But only if they have ascended already, as we can see with Davepeta, their shirt has the Time Cog, but not the Heart Symbol, because Nepeta wasn’t a God Tier. They may still gain basic powers or traits of those Classpects though- Such as Davepeta combining Time and Heart to bring us a lovely Undertale reference, because as we all know, Heart + Time is very much the definition of Determination.

Also do NOT prototype your God Tier self as a First-Prototyping through Time Shenanigans, or you will give every Underling God Tier powers.