Here's an interesting article on the relationship between gut microbiome and sleep for those who are interested in this topic. It's not specific to RLS but does mention sleep disorders generally.
mdpi.com/2072-6643/16/14/22....
It concludes:
Consuming a varied diet comprising foods abundant in dietary fiber, polyphenols, and unsaturated fatty acids can exert a favorable impact on the gut microbiome, potentially influencing sleep patterns. Metabolites synthesized by the microbiota, such as short-chain fatty acids (SCFAs), gamma-aminobutyric acid (GABA), serotonin (5-HT), melatonin, and tryptophan, play crucial roles in modulating physiological functions, including sleep regulation. Imbalances in microbiota composition may be associated with the onset of sleep disorders as well as other chronic conditions, including obesity, cardiovascular diseases, and mental disorders.