assigning values with incompatible dtype

The behavior of xarray when assigning values with incompatible dtypes is a bit arbitrary. This is partly due to the behavior of numpy.... numpy 1.20 got a bit cleverer but still seems inconsistent at times... I am not sure what to do about this (and if we should actually be clever here).

1. Direct assignment (dupe of #4612)

import xarray as xr
import numpy as np

arr = np.array([2])

arr[0] = np.nan
# ValueError (since numpy 1.20)

arr[0:1] = np.array([np.nan])
# -> array([-9223372036854775808])

da = xr.DataArray([5], dims="x")

da[0] = np.nan
# <xarray.DataArray (x: 1)>
# array([-9223372036854775808])
# Dimensions without coordinates: x
(because this gets converted to da.variable._data[0:1, 0:1] = np.array([np.nan]) (approximately).

da[0] = 1.2345
# casts constant_values to int

2. Via a numpy function (pad, shift, rolling)

pad

da.pad(x=1, constant_values=np.nan)
# ValueError: cannot convert float NaN to integer

da.pad(x=1, constant_values=None)
# casts da to float

da.pad(x=1, constant_values=1.5)
# casts constant_values to int

da.shift(x=1, fill_value=np.nan)
# ValueError: cannot convert float NaN to integer

# da.shift(x=1, fill_value=None)
# None not allowed by shift

da.shift(x=1, fill_value=1.5)
# casts fill_value to int

da.rolling(x=1).construct("new_axis", stride=3, fill_value=np.nan)
# ValueError: cannot convert float NaN to integer

# da.rolling(x=1).construct("new_axis", stride=3, fill_value=None)
# None not allowed by rolling

da.rolling(x=3).construct("new_axis", stride=3, fill_value=1.5)
# casts fill_value to int

To check:

• What does dask do in these cases?
• What does pandas do?
• What about str dtypes?

Reproduce the listed DataArray assignment, pad, shift, and rolling cases, then compare their behavior with NumPy, pandas, and dask as requested. A complete contribution needs an agreed policy for incompatible and string dtypes, followed by tests covering the chosen behavior; the issue does not name files or tests.