As another person in perimenopause, I too am dealing with sleep issues. I was just talking to my OBGYN about it yesterday because I truly don't want to become a slave to any kind of meds or supplements. So, I'm trying to take a more basic approach for as long as I can handle it.
While I am mainly doing it because I let my body go after being sedentary for a couple of prolonged periods from health issues and had a bout of mild depression in the mix, I am trying to get my fitness routine back up to speed. The more I work out and move around during the day, the more tired I am when it's time to sleep. Improving my diet is probably also helping. I also don't do any caffeine after 7pm.
Falling asleep is rarely an issue, but I'm routinely waking in the middle of the night and finding it hard to doze back off. Before I go to sleep, I make sure my conditions are ideal for my preferences. For example, I need moving air (ceiling fan on), noise (I have an app where I can created mixes of soothing noises), and blankets (I prefer big heavy blankets...even when it's warm outside). Still, if I wake...while I won't indulge in screen time, I may put on my headphones and jam out to some music and slowly shift to more somber stuff just to work myself up a bit so I can get tired again. I know I'm on the right track if I start getting groggy by song 3. I know this may seem so cliche, but counting things also helps. No, not sheep, but I'll start counting things I own or have done in greater quantities. Last night, I was counting off all of the places I've been that have staircases.