I just paid a nice penny for some Botarga. I'm wondering what the storage guidelines are for storing this after I open the original packaging

Bottarga will keep for MUCH longer than a week. Wrap it well, store it in the refrigerator and it should last for months.

They also share a recipe if you want me to paste the link for you.

A Los Angeles Times article states, "Bottarga is typically vacuum-packed for export. Once you have opened it, do not keep it exposed to air for longer than necessary. Wrap the piece you do not use in lots of plastic and store in the refrigerator for up to a week."