It would make sense to try to implement somehing similar as suggested by UN happiness report to provide comparability with more general findings. If i remember correctly, it was 1-10 scale based on day-to-day feeling of happiness.
I don't think such a questionnaire exist but you can used a quality of life scale wich include a social functioning component or dimension as the SF 36. This is less simple as what is proposed by Jan-Erik (he have a good idea) but more precise and robust to publish the results.
Phu, Becky, and Alan J. Gow. "Facebook use and its association with subjective happiness and loneliness." Computers in Human Behavior 92 (2019): 151-159.
Kırcaburun, K., Kokkinos, C. M., Demetrovics, Z., Király, O., Griffiths, M. D., & Çolak, T. S. (2019). Problematic online behaviors among adolescents and emerging adults: Associations between cyberbullying perpetration, problematic social media use, and psychosocial factors. International Journal of Mental Health and Addiction, 17(4), 891-908.
Hughes, N., & Burke, J. (2018). Sleeping with the frenemy: How restricting ‘bedroom use’of smartphones impacts happiness and wellbeing. Computers in Human Behavior, 85, 236-244.