Does the Sai Satcharita mention Udi being effective for sleep-related problems like insomnia?

Yes, Chapter 33 provides two distinct examples of Udi curing insomnia, as noted by Hari Sitaram Dixit. In the first case, a friend of Dixit's who had been unable to sleep for eight days despite taking medicine found immediate relief. After taking the Udi just once, he slept soundly through the night. In a similar instance, another friend's child from Bandra had not been able to sleep for two months. The father took the child to Shirdi for Baba's Darshan, and that very night, the child got sleep and continued to sleep well thereafter, demonstrating Udi's power to restore natural rest.