I quickly tested it on Linux. It looks like on Linux it is indeed works as rootless Docker.
So you need to confiugure the subuid and subgid files and if the lowest userid after the username is 100000, then it is UID 1 inside the container. 100001 is UID 2 and so on. On the host, you have to change the owner of the files and folders to 100100 for example (depends on your subuid setting), because if your user is the owner, that is root inside the container. If any other user which is not in the range of allowed UIDs, it will be nobody in the container.
Or… You could simply install Docker CE instead of the desktop and you can be sure that UIDs inside the container will be the same as outside.