I have done a study using factors of relatedness, self-efficacy, mindset, and task relevance with students in T-K12 public schools (n=2,908). An interesting finding is that the variables differ based on cultural identity. The results of the study supported the literature in this area. The need for relatedness in the domain of self-efficacy in the classroom may not be equal for all.
Your question regarding relatedness can be further refined to include the context in which you are inquiring as self-efficacy, mindset, relatedness, and other psychosocial variables are domain specific.
Hope this information helps focus your question and guide additional literature review to help in your research inquiry.
Let's go further and see if there would be any case studies or narrative inquiries using SDT kind of theoretical frame as a part of interpretation or the inquiry process?