Are you interested in linguistic correlates of self esteem for the purpose of linguistic research?
Or are you looking for a practical way to measure self esteem?
There may be linguistic factors, but I would suggest looking at psychology research instead of linguistics narrowly for a practical answer. The (United States) NIH (National Institute of Health) has various surveys/packages designed to measure development, behavior and cognitive/psychological status for things like language development, depression, and so forth. These are often available for free online. They sometimes take relatively extensive testing (maybe an hour or two?) and are done individually, but they are used by psychologists and medical doctors to evaluate certain outcomes or conditions, and are widely tested and standardized (at least within the US context). That approach, or something like it, will be much more reliable and practical than looking for potential linguistic correlates of self esteem. They are also very often used for academic research too, not just practical applications. I don't know if there is a specific test battery designed for self esteem (I've only encountered these in passing for my own research, such as measuring memory abilities), but you probably can get some information that way, or at least think about how to design your own materials.