I took a deep dive in my wireshark trace and it seems like the Apple Device simply doesn't fullfill the User request in a prioritized way. It seems to follow the IMAP rfc2177 (as by my limited understanding) correctly - but it simply waits for *itself* to mark the IDLE as *Done* (Which can take several minutes or longer) until it even requests the the message which the user requested earlier on the iPhone display. I currently don't think this is a dovecot bug, but I do that only as a hobby and I am not deep into dovecot or imap.
Again the screenshot from before - the red rectangle marks the time the iPhone needed to even start to request the message from the dovecot server. I requested the message via touch press before this time on the iPhone. https://drive.google.com/file/d/1jTajdI6XDTAXNZVUdE1VYLeXi8S6jreA/view?usp=s...