Why the upper level was called a spardeck

Does spardeck refer to the spare masts, yards, and spars stored at that level?

Yes. The name came from the level where spare spars, yardarms, and similar rigging components were traditionally kept.

Spars included replacement masts, yards, and related long pieces of rig. Ships needed to carry them where the crew could reach and handle them. The level used for that storage acquired the name spardeck. Later designers could build a more continuous fighting deck there while retaining the older functional term.