Equality between datetime64[s] and datetime64[ns] is not consistent for coordinates vs data variables

What happened?

When the datetime resolution of coordinates differs, this breaks equality via .equals:

datetime_ns = np.array(['2025-01-01'], dtype='datetime64[ns]')
datetime_s = np.array(['2025-01-01'], dtype='datetime64[s]')
da_ns_coords = xarray.DataArray(dims=('x',), data=[0], coords={'x': datetime_ns})
da_s_coords = xarray.DataArray(dims=('x',), data=[0], coords={'x': datetime_s})
da_ns_coords.equals(da_s_coords)
=> False

But not via .broadcast_equals:

da_ns_coords.broadcast_equals(da_s_coords)
=> True

For data variables, equality via .equals holds even when the datetime resolution differs:

da_ns = xarray.DataArray(dims=('x',), data=datetime_ns)
da_s = xarray.DataArray(dims=('x',), data=datetime_s)
da_ns.equals(da_s)
=> True

What did you expect to happen?

I expected the two values to be equal even when the dtypes are datetime64[ns] vs datetime64[s].
At a minimum, I expected the treatment of dtypes in equality to be consistent for coordinates vs data variables, and for .equals vs .broadcast_equals.

Minimal Complete Verifiable Example

See above.

MVCE confirmation

• Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
• Complete example — the example is self-contained, including all data and the text of any traceback.
• Verifiable example — the example copy & pastes into an IPython prompt or Binder notebook, returning the result.
• New issue — a search of GitHub Issues suggests this is not a duplicate.
• Recent environment — the issue occurs with the latest version of xarray and its dependencies.

Anything else we need to know?

I suspect the cause is that pandas DatetimeIndex is not .equals when the dtype differs:

index_ns = da_ns_coords.indexes['x']
index_s = da_s_coords.indexes['x']
index_ns
=> DatetimeIndex(['2025-01-01'], dtype='datetime64[ns]', name='x', freq=None)
index_s
=> DatetimeIndex(['2025-01-01'], dtype='datetime64[s]', name='x', freq=None)
index_ns.equals(index_s)
=> False

Environment

Start by running the MVCE comparing DataArray.equals and DataArray.broadcast_equals for datetime64[s] and datetime64[ns]. Trace the equality entry points and coordinate index comparisons, then add regression coverage showing consistent results for coordinates and data variables. Done means equivalent datetime values compare equally through both methods.