Incredibly common. Incredibly frustrating.
Your energetic systems started synchronizing when you connected, and now they’re in discord. Insomnia is often a spill-off from your telepathic connection. During the day, this can get dulled into the background by the 3D world and its many, many distractions. At night, we can feel their presence missing a lot more, and there’s less to distract us from it.
The 3-5am window is when the veil thins. Your energy body is trying to connect with their higher self during sleep - that’s its natural state when it’s free from conditioning. But your physical body needs rest, so you’re caught between these two needs.
What you’re describing with feeling their energy and not being able to control it - that’s the heart chakra activation creating this sense of fullness in your chest that makes settling down nearly impossible. Some twins feel actual heart palpitations that jolt them awake, even when they do fall asleep.
This is part of the balancing process, but I know that doesn’t make the exhaustion easier. Your body is trying to handle new energetic loads it wasn’t built for.