I'm really curious what word Sarashina-sensei uses in the raw that was translated to "partner". It's such a delicate, nuanced phrasing that I feel like it would add a lot of additional insight.
In particular the usage of "partner" is quite interesting since I find that it's often a default term used in BDSM circles. Relationships can be complicated and since it's a community where polyamory and other forms of non-monogamy are quite common as well it's often a middle ground that implies "I have an ongoing relationship of some sort with this person". It could be purely BDSM (like Nana and Kaoru tell themselves), purely sexual, FWB, romantic, married, unmarried but in a long-term relationship... whatever. The relationship could be hard to define or you might want to refer to people who fit into various categories. It doesn't matter. You're saying that you're more than simply friends, but not giving further details. Which is interesting because in many other contexts the term is more often used to mean "a serious, long-term romantic relationship". These are complex terms and not everyone uses them in the same way.