Between the bugged apartment and reporting to Fury, I'd still call it spying. And because nobody, including her, thought to mention her being related to Peggy till the funeral.

[ It didn't take much digging into history books to know that Margaret Carter had been important to Captain America. Fury might have thought it was perfectly fine assigning her niece to keep any eye on him, but Steve had felt like an idiot twice over before everything came out. ]

At least she wasn't doing it for HYDRA.