There are multiple companies who sell compostable coffee cups, lids, and sleeves. Circling back to all food packaging needing to be made from bio-based materials, the coffee cup is the next most used commodity that would compost easily if the infrastructure and education were present. Until we create the system where the consumer receives and understand product end-life management aside from landfilling, the problems that exist today will only continue. Once composting becomes the norm for food based products and packaging, we will see the elimination this type of "waste" and instead, we will see the material as food for another process with embedded value.
This solution was suggested by Marco from Italy
Ecoffee Cup is a reusable takeaway cup. It is made with bamboo fibre (as well as corn starch and strengthening binder*). The lid and sleeve are made with matte food-grade silicone which is designed especially for hot liquids.
You can buy here https://ecoff.ee/collections/reusable-coffee-cups
Solutions: Cup club
This solution was suggested by Tamar from England
Use a reusable cup that can then be returned at a local coffee shop/ drop off station where they will get collected washed and redistributed to cafes. It's like using a keep Cup but without having to remember it and carry it around every day.