I feel like when people talk about right to privacy they're often using a catch-all for several different concepts. There's a big difference between a right to anonymity and a right to be forgotten.

If you have a very strong right to anonymity, a right to be forgotten is less important because it's easier to separate yourself from your online identity. In fact, forgetting information is pretty harmful because anonymous systems need better tools for building and validating reputation.

If you have a strong right to be forgotten, anonymity is less important because you can just delete information you regret sharing. And similarly, anonymity is kind of harmful because you now need ways to validate who owns information and ways to control how it's spread.

EU seems to be less concerned with anonymity, and more concerned with managing and regulating information after it's already been created and shared. This also kind of rubs the anonymity crowd the wrong way because they've advocated for a while that information isn't necessarily something that you can own like property, and that the Internet should actually be far more immutable than it already is.