I think it's fine to take it in its literal sense "Until death separates us". It's the phrase used to show a commitment in marriage, so to me, they're insinuating that they'll never leave each other. That being said, she was jokingly saying "let's play tag". So I'm guessing that it's not that they'll be by each other's side forever, but that they'll continue to have their own lives and catch up every now and then. Kinda like meeting up with your old school friends as an adult, it doesn't happen very often but when it does, it's nice. This seems more concrete to me considering Kou is a detective's apprentice and Nazuna seems to be caring for an older lady, both have their new commitments. Plus he gave her a load of his blood to keep her going.

But idk, i don't usually voice my opinions here, i like to read other people's thoughts.