Thank you so much for the explanation.  That helped me a lot.

> So depending on whether N is odd or even the rest of the text will be
> highlighted with `font-lock-string-face` ;-)

Well that explains the behavior I saw during my experimentation!

I've managed to find a solution for propertizing. However I've now I have a new
issue that I don't understand. When editing a line inside the heredoc the line
changes to white font then shortly after changes to green.  What would be the
cause of that behavior? I'm not really sure where to begin debugging.