No, the new legislation's notices only are allowed to be exercised in order to fulfil the requirements of a warrant (or similar instruments that have judicial oversight).

Don't get me wrong, mandating crypto backdoors is obviously a brazen breach of privacy and opens the doors to all sorts of abuses. But plaintext systems like Fastmail won't be affected by the new notices because a warrant was already sufficient to get access to your plaintext emails.

FWIW, as currently legislated, the "backdoor" scheme still requires warrants to be issued for data captured under it.

Yes, that. The law allows for requiring new backdoors to be requested up-front, but still requires warrants to activate those backdoors for specific requests, and it still doesn't give firehose access. It's not as awful as it's made out to be by some, but it's still pretty ham-handed in some of its implementation, and that's what we're proposing they look at changing.