Refactor update coordinates to better handle multi-coordinate indexes

[benbovy]

• Closes MultiIndex coordinates do not exist updating v2022.3 to v2022.12 #7563
• Closes Update assign_coords with a MultiIndex to match new Coordinates API #8039
• Closes overriding coordinates with assign_coords does not drop indexes #8056
• Closes drop_indexes is reversed by assign_coords of unrelated coord #7885
• Closes Error when adding a DataArray to an existing Dataset with a MultiIndex #7921
• Tests added
• User visible changes (including notable bug fixes) are documented in whats-new.rst

This refactor should better handle multi-coordinate indexes when updating (or assigning) new coordinates.

It also fixes, better isolates and better warns a bunch of deprecated pandas multi-index special cases (i.e., directly passing pd.MultiIndex objects or updating a multi-index dimension coordinate). I very much look forward to seeing support for those cases dropped :).

[dcherian]

Can you check if this benchmark regression is real

indexing.AssignmentOptimized.time_assign_no_reindex

[benbovy]

@dcherian the benchmark regression is fixed.

I think this is ready for review.

Regarding the multi-index deprecation warnings: there are still a lot of places where pandas.MultiIndex objects are passed around directly as coordinates in xarray's internals (both code and tests). They may also be promoted indirectly as in swap_dims(), which doesn't show any warning when this occurs. I will fix that in a follow-up PR.

[dcherian]

I can't review the code really but have suggestions on the warning message.

Can you silence these two:

xarray/tests/test_variable.py: 1 warning
xarray/tests/test_dataset.py::TestDataset::test_constructor_with_coords

I think the warning should show the syntax for "passing it as coordinates"

 If you want to keep this behavior, you need to first wrap it explicitly using `mindex = xarray.Coordinates.from_pandas_multiindex()` and pass it as coordinates with
`Dataset.coords['x'] = mindex` or ``DataArray.coords['x'] = mindex

[benbovy]

Can you silence these two?

Do you mind if I address this in a follow-up PR? I started silencing warnings (there are a few dozen more in the tests!). Also there are still quite many cases where the warning should be emitted but is not (e.g., passing pd.MultiIndex as DataArray coords). This will need more review that is out of the scope of this PR.