It looks weird to have a different background for the SDDM and another for the lockscreen.
I'm afraid this isn't generically possible due to differences in capabilities between SDDM and the lock screen. SDDM only supports a single image; the lock screen supports slideshows, picture of the day, and arbitrary QML plugins.
Understood. Was ever considered the possibility of developing a "kdm" (K Display Manager) to offer deep integration with KDE?
In fact KDM used to exist in the past! I don't know the history of why it was dropped in favor of SDDM. It was before my time.