The hormone melatonin helps regulate sleep and wake cycles. It's often used by people  with insomnia or that just want to sleep 'better'.

What does melatonin do on a biochemical level with skeletal muscles so they feel 'sleepy'?

Melatonin is a hormone produced in the brain by the pineal gland.  Its effects are expressed in the brain rather than the muscles.  You can access further details via the Wikipedia link I've provided herein.  I hope this helps.

What doesn't melatonin do? Check out the Journal of pineal research: https://onlinelibrary.wiley.com/journal/1600079x

They often have free to access articles and the abstracts are worth reading to get an idea of what melatonin does.

The circadian function is a small part of it's role. Incidentally most of the melatonin in your body is found in your gut.