Backend is a general word, not limited to client-server or the web. You can have a rendering backend with various configurable choices, like in Matplotlib (https://matplotlib.org/stable/users/explain/figure/backends....), or the deep learning library Keras has a choice between PyTorch, JAX and TensorFlow backends.
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.