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What you're describing is perfectly normal for you two cuties
Since they're scared of their new surroundings and still settling in, it's likely they'll cling together and be apprehensive of exploring for a little while. They can sleep like that, and some budgies carry this quirk onto their later lives, also.
You may not see them eat or drink for a day or two, and that's okay, too.
Soon, they'll settle in and each choose what perch they like to sleep on. For now, you can cover their cage on three sides during the day to help them feel safer, make sure you leave music on whenever the house is quiet (silence is danger to budgies) and talk to them gently so they can see you're not a threat.
I'm sure your little budgies will be very happy with their new home! What are their names?
It's great to have you with us and we look forward to hearing all about your little budgies in the future, as well as seeing some pictures when you get a chance.
Feel free to ask any questions at all you may have as we're here to help!
Hope to see you around!