I wouldn't call it background unless maybe it's async or continues to process stuff while you're doing other things.

what's the backend of a spreadsheet engine going to be doing? updating the datastructures of the spreadsheet.

is it going to be local or remote? that's not part of the question.

is it foreground or background? that's an implementation choice. apple II, yeah, everything freezes while it recalcs. windows? recalcs when it can, don't let the mouse freeze.