In general, unless you and your correspondents are using PGP or some such, your email is readable by anyone who can obtain a search warrant in the country where your email provider resides. (Protonmail may or may not be an exception [2]).
[1] https://www.fastmail.com/help/ourservice/security.html
[2] https://www.wired.com/2015/10/mr-robot-uses-protonmail-still...
However there are some other worrying changes like the fact that TANs and TARs are secret and have no judicial review. Warrants (even the new computer access warrants that were passed in the same bill) have judicial review. But at the end of the day, they'd be serving a warrant to fastmail, not you.
Personally I use mailbox.org, and one of the really nice features is that you can give them a PGP public key and they'll encrypt everything you receive. So in the case of a warrant (though Germany has different laws on that matter) they could, at most, get the contents of new emails.
There are a couple of things I don’t like about Posteo (as a customer):
1. It recycles deleted addresses/aliases after six months and makes them avaiufor someone else to claim and use. Ideally, this should be never done to protect customers. Fastmail also recycles deleted addresses/emails within a few months (sooner than Posteo does, IIRC).
2. It provides only two aliases in the base pricing and additional aliases (if many are required) will increase the cost. Fastmail provides 600 aliases in every plan! So if you’re heavy on aliases, Fastmail would be cheaper.
Other providers similar to this that I haven’t subscribed to, but you can read up on or try, are mailfence (has a free plan as well), runbox and mailbox.org. All of them have been around for quite sometime and also provide IMAP access (which is important if you want to migrate email content from one provider to another).