Part of the discussion in #5329. I'm opening this issue to make the discussion on this topic a bit more focused.

As mentioned in #5329 (comment), we need to find a way to

• construct a repr that includes the metadata from all levels of nesting?

Simply including the repr of the wrapped array usually results in reprs that are way too long, so instead we could introduce a protocol (or method) that returns a mapping of type names to metadata, and a function to call that protocol. If a duck array does not implement the protocol, the default would be to return {typename: {}}.
For example calling repr(arr) where arr is a xarray(pint(dask(sparse))) would make xarray call the data's __metadata__ and use that to construct it's repr. This could be something like

def __metadata__(self):
    wrapped_metadata = self._data.__metadata__()
    metadata = {
        "a": str(self.a),
        "b": str(self.b),
    }
    # or something like {**wrapped_metadata, **{type(self).__qualname__: metadata}
    return wrapped_metadata | {type(self).__qualname__: metadata}

In the example, the result of the first call could be something like:

{
    "sparse.COO": {"shape": (30, 1000), "dtype": "float64", "nnz": 768, "fill_value": 0},
    "dask.array.Array": {"chunks": (10, 100), "shape": (30, 1000), "dtype": "float64"},
    "pint.Quantity": {"units": "m", "shape": (30, 1000), "dtype": "float64"},
}

with that, xarray could either manually format the repr or use a helper function (which should probably have a max_width parameter).

This doesn't work for duck arrays wrapping more than a single duck array, though. Also, I'm not sure if the type name should be the type's __qualname__, and if shape and dtype, which every duck array has to implement as properties, should be included.

xref pydata/xarray#4324, pydata/xarray#4248