While "stack away" is literal, related "stack" idioms carry different weights in conversation:

To compare or measure up against something else (e.g., "How does this new model stack up against the competition?").

"Stack away" is a phrase with dual identities: it is a common English phrasal verb meaning to store items for future use, and more recently, it has become the title of a popular mobile puzzle game. 1. The Mobile Game:

If a card does not have a matching tray, it is sent to a "waiting area." If this area overflows, the game ends. This adds a layer of management where players must prioritize which colors to clear first.

Players are presented with stacks of colored cards in the center of the screen. The objective is to rotate these stacks 360∘360 raised to the composed with power

Stack away - Definition, Meaning & Synonyms - Vocabulary.com

In general English, "stack away" functions as a synonym for "stash," "store," or "put away." It implies organizing a large number of items neatly into a designated space for long-term storage.