Depends what you mean by 'general supplement' but a majority of people are deficient in magnesium (~400 mg/d is the recommendation) and its ubiquitous involvement in hundreds of enzyme systems might reasonably indicate that a positive role in normal sleep patterns could be expected as reported in a number of publications. If there is no benefit then other factors are likely to be to the fore.

I am just reporting on available literature, like this:

https://pubmed.ncbi.nlm.nih.gov/35184264/

"Observational studies suggested an association between Mg statuses and sleep quality, while the RCTs reported contradictory findings."

Have you tried calcium glycinate next?