Maybe I'm missing something, but what "daemon-style" app tasks are you doing, or expecting, with KDE Connect? Its core functions seem to be quick tasks; sending files, clipboard, remote control, etc.
Perhaps my usage is basic in this way - I've never had an issue with using the iOS app as it is.
Legacy KDE apps used to follow this naming convention until the late 2000s, early 2010s.
You had apps like Konqueror (web browser, file manager), KMail (email client), Kompose (music score editor), KImages (later rebranded to Krita), and KDevelop (software dev IDE).
Modern KDE apps dropped the 'K' prefix and moved to a more recognizable scheme, like: Falkon (web browser), Dolphin (file manager), and Okular (document viewer).
As you can see, its now a mix of whether the app keeps the 'K' in the name. Some do not.
Same use case, its also been very useful for copying and pasting text from my Mac to the Steam Deck, similar to Universal Copy and Paste between Apple devices.
Perhaps my usage is basic in this way - I've never had an issue with using the iOS app as it is.