Move storing logic to background script

[sharon-wang]

Currently, all of our storing logic exists in storage.js and is executed by the content script being run on the active tab. However, this may pose some issues since all tabs write to the same browser local storage and the stores occur asynchronously. The asynchronous stores may give rise to incorrect data, as data may get overwritten.

If we move our storing logic to our background script, then we can coordinate saving to storage across all tabs and avoid the problem of multiple tabs asynchronously writing to the same storage.