I do enjoy the idea of Eris and the Guardian having such a relationship, but it is purely fanfic. Within the base narrative, it is implied heavily that the relationship between Eris and the Guardian is more akin to siblings, or brothers in arm. Simply put, throughout the entire series, the Guardian has been a tool and a weapon for Eris to enact her revenge. That is not to say she is manipulating us, rather, as much as she is using us as her blade, we also wish to be her blade. Such a relationship could never support romantics. It’s part of the reason we did not know where Eris disappeared to, but at her behest, we did everything she needed of us.