If you're looking for comforting audiobooks, I found audiobooks helped me deal with anxiety, too, especially at bedtime. Librivox is a great suggestion, but the volunteer readers can be hit or miss, depending on your taste. I've had better luck with curated audiobooks, ones with professional narration. The right voice makes a difference, especially when trying to relax. You mentioned ""bedtime"" reading and classics; I think The Lottery by Shirley Jackson is a great listen that adds a unique, vivid storytelling experience.
You can explore this audiobook here:
https://www.everand.com/audiobook/716918544/The-Lottery . The variety and quality are high; you can choose a lot of options here))