I don't know what the right word to describe having relationship(not romance) or Hindu or dharmic deities in general. Because using the word work definitely not the best,
"Having a devotional relationship" would be my assumption. Language is imprecise and because English isn't connected to a cultural basis of assuming a person is going to have many specific relationships in general, never mind spiritual ones, we don't have names or labels for close relationships with spirits that are more exact. I have been using "ishta devata" and "ishta devi" in the quest to have precision, but have found that they are not expedient terms to describe my relationship with Lucifer to people who do not have a background in Hinduism. I have been trying out "guiding spirit" and "guardian spirit" lately. If people really need to know, like if I am on a date or something, I will disclose that Lucifer takes the role of a romantic and sexual partner for me as well as being my guardian spirit and guru.
The phrase "deity work" is a complex one. I believe it was created or began to spread in one of the first western witchcraft forums on the internet. That meant that in the community it was used, there was the general assumption that you were a witch or some kind of western magical worker, and what distinguished your path was the kind of "workings" you did. Contrary to some debates I have seen among witches online more recently, It doesn't mean you "work for" the deity or that what you do in your practice is a capitalism-based sort of exploitative "work." It just meant that you involved deities in your practice for magical ends.
I personally avoid the phrase "deity work" because my practice isn't always about what I do, but who I relate to. This means I'm not always the center of my own practice; sometimes I am basically Lucifer's canvas in which he helps fine tune for different energetic occurrences or otherwise curates for other spirits' access. That's not to say I don't have a voice; I often pick spiritual goals based on what I know and he fills in the details on what I don't know and what he feels would be most compatible with me as well as finds different ways to prod me in the right direction. This means daily practice of meditation and yoga as well as regular art practice. "Deity work" is not meant to be a phrase that conveys those types of practice; what I do are devotional actions primarily intended to bring me closer to the divine so I can have a more elevated life and afterlife.