I have a Local variable saved in my "Design System v2" file. This file is published as a Library for use in other files, it's available to be used.

Unfortunately that variable is not viewable in the "Local variables" panel, only when I click into the variable button, in this case, in the Corner Radius field, the variable is viewable... Seems like they are still working out some kinks, perhaps some feedback for the Figma team

You're right! They were there to publish in the assets panel and readily available to use in my other files. I should have figured they wouldn't be under "Local Variables", but it wasn't obvious they would be available to apply in relative places. Thanks!

I feel like there should be a "Global Variables" area within projects.

100% Agree. Ive only just begun using variables but I will submit a ticket to the Figma team to leave this feedback. Similarly to how the Assets panel contains Global Components from all of your Libraries, there ought to be a place for "Global" variables, sorted by Library name