From my experience the “default” experience, which is Docker Desktop, is a pain, due to what you described. In particular, Linux containers and Windows file permissions just don’t mix well.
Other than that, there’s three options:
Docker Desktop, but used from WSL 2. This seems to be the cleanest solution nowadays. Never personally used it though. Officially supported.
Installing Docker inside WSL 2. Configuring this correctly is a bit of a pain and not really supported AFAIK.
Installing Docker in a VM, using the integrated Hyper-V functionality for example. The least amount of integration, but most reliable.