It just looks simple. I still don't know exact reason why that bug exists. I haven't managed to write a shorter example that reproduce that behavior.
Resolution came to my mind after reading QClipboard docs, to be precise this fragment:

it is recommended that the contents of the clipboard are stored or retrieved in direct response to user-input events, e.g. mouse button or key presses and releases. You should not store or retrieve the clipboard contents in response to timer or non-user-input events.

Obviously, KDE Connect doesn't follow that recommendation and I think that running KIO::pasteActionText after main loop start doesn't follow it too.