"We are seperated" means that she doesn't have to feel guilty about how she is treating you because she is no longer committed to the marraige. She is free to have affairs, not communicate with you , be rude, etc, because she is "Seperated".
I have had to explain to my W, the she is not "Seperated" until we are divorced. Right now, these are just simple, low class, affairs.
I notice when rent is due, she does not step forward with the %50 that my prior "roommates" had paid. Nor, will she be "Seperated" when I submit my benefits paperwork for health insurance next Jan. At these times, she is fully married.
I assume PON that this is pretty much what your W means also.