Is the public_folder a global option or folder collection option?

Global option.

You cannot use a relative path ('' or '.') with the global public_folder option. It’s supposed to start with /. You should be able to use a relative path with the collection-level public_folder option.

The double slash with '/' is probably a bug. I’ll fix it.

And can't there be some way to store the value without a leading slash?

A relative path with collection-level public_folder option works when the path option is used (for Hugo’s page bundles). In that case, a leading slash can be omitted with '' or '.'. It’s an entry-relative path.

Otherwise, the path is always root relative, starting with /.

When I use public_folder: /, I’ll get image: example.jpg instead of image: //example.jpg, but it’s a bug anyway... I’m fixing it.

The issue with public_folder: / is solved with v0.53.2. Later I’ll add config validation for the empty or relative path.