A Steinberg person clarified the non-relationship between Score Editor lyrics and Omnivocal lyrics (which go in a text field, not a lyric field):
My interpretation of this comment, coupled with your observations, is that the text field is just like a text instruction in the Score Editor, not lyrics, though perhaps the horizontal positioning of that text may be close to how it would be if it were a lyric?
To be honest, I’ve never used Cubase’s score editor for lyrics – I only use it as a visual aid for editing MIDI, with the score editor on one screen and key editor (for the greater control on editing) on the other.
I do use Dorico for making lead sheets, but, even if I’ve got a melody track in Cubase while working out an arrangement, I don’t bother importing that into Dorico as I want more precision in entering the lead sheets the way I want them, and what I’ve played will be more feel-oriented than printed notation precision-oriented. If I want a lead sheet for tracking vocals at all (I’m doing my own vocals on my own songs, and I’ve often played them live a fair bit before recording the songs so just need lyrics), I’d also have been using the lead sheet prior to that point for refining the melody and phrasing on the songwriting front. (I’d never done that with Finale as Finale was too much of a pain to use when making adjustments along the way, so I only made lead sheets after a song was completely finished, and usually that was after having recorded it.)