I can't feel any romantic intent from Nazelbert when proposing but in the context of everything that's happening it is still a very sweet moment.
He is trying to look after someone who was willing to help him at such a horrifying moment in his life, now knowing they were in a situation way more precarious than he had been before, and knowing it is a hard situation for both, still decides to ask if she'd like to go along with his plan.
It's kind of weird still since they have basically no options left, plural - nazelbert's condition for the alternative on the royal mandate for some reason still has him marrying her so he probably wouldn't be given governance of the frontier, leaving his fate in the air; and with MC's original plan of living in a monastery dashed she has no real place to try and go immediately -, so it's kind of an extremely unbalanced choice there for either party, but thankfully it is still played rather sweetly.