Could be it's not actually separation anxiety but anxiety about being in the crate....that experience is still too recent. Hopefully, she'll grow out of it.
We have no idea of Sunnie's past...except that she was at the shelter for a month and a half (some earlier bit in a foster situation). She is petrified of the crate. Wants nothing to do with it. Was she ever crated before? I have no clue. But a big part of me thinks it's because she was crated at the shelter and...knowing how she is with noises and activity....the shelter scared the bejeebies out of her.
I can get Sunnie settled in a crate only if Dan is in there with her. Needless to say, that doesn't happen often. (Actually, we dismantled the crate and have it folded up and set aside "just in case".)