Daily exercise knocks on both doors, so to speak. It will help you sleep and it will also help you manage anxiety. Same for maintaining gut health. We are non-orthogonal systems.
What I mean to say is that first things first. There are lots of well-meaning advice we can give to people suffering from insomnia, delayed sleep onset etc etc. Most of it will only work if it helps fix anxiety. Awareness of this can be very helpful by itself.
Edit typo while on my trainer. Lol
Sleep gives immediate benefits, exercise gives longer term benefits. It's a conundrum.