Whenever you post something publicly on the internet, it's best to assume that you may not be able to delete it. Scrapers, search engines, caches, people taking screenshots, ... This is of course especially true with the fediverse, where posts are duplicated across servers. (Typically deletion requests are honored, but they might not, or they don't go through because of an issue, and even then the previously listed issues are still present.)

However, this is only regarding information that's either public or shared through the protocol, which doesn't include your IP address or the email address used to register. These are only available to the server your account is on and the client you connect with, if you're using an app. This information is I believe what OP was asking about, not the posts themselves.

(Without a proxy / VPN (comes with its own up- and downsides) your internet provider can also check some of your internet traffic, such as who you're connecting to, though typically not what data is being exchanged, due to encryption, like HTTPS.)

whoever is listening does not have to obey the delete request

Say it louder for those in back. I kept getting downvoted when I said that the GDPR won’t help them on the fediverse as there are instances in places it won’t help.