Strength-based therapy has a thinner evidence base as a named standalone treatment, because it is more often a stance therapists bring to other work than a protocol with its own trials. Related research on resource-focused adaptations of therapy, and on character-strengths interventions, is what exists, and it is still uneven in quality. Those studies are worth reading as studies of those methods, not as proof that a label called strength-based therapy is a cure for low mood, shame, or self-criticism.
Munder, T., Karcher, A., Yadikar, Ö., Szeles, T., & Gumz, A. (2019), Zeitschrift für Psychosomatische Medizin und Psychotherapie. A systematic review and meta-analysis found that resource-focused adaptations of cognitive-behavioural and psychodynamic therapy were associated with small to moderate advantages over comparison treatments, while noting small samples and risk of bias in many of the included studies.
Yan, T., Chan, C. W. H., Chow, K. M., Zheng, W., & Sun, M. (2020), Journal of Advanced Nursing. A systematic review of character strengths-based interventions for people living with chronic illness was associated with improvements in self-esteem and self-efficacy and with reductions in depression. This studied a positive-psychology intervention, not weekly strength-based psychotherapy as a brand.
Franklin, C., Zhang, A., Froerer, A., & Johnson, S. (2017), Journal of Marital and Family Therapy. Process research on solution-focused brief therapy found the most empirical support for strength-oriented techniques in session. That is adjacent evidence about using strengths in conversation, not a trial of strength-based therapy as its own model.