Reimplement Datatree typed ops

[TomNicholas]

Follows on from #9589, but for the ops defined in _typed_ops.py.

Does this mean we can remove most/all of datatree_ops.py?

EDIT: Answering my own question - none of datatree_ops.py is currently used since we disabled it. It does contain lists of methods we should implement, many of which are now implemented in this PR and #9589. As the only purpose it serves right now is tracking remaining un-implemented methods, we should probably remove it in favour of creating a new github issue.

• [x] Closes #8963, and also https://github.com/pydata/xarray/issues/9365#issue-2466498386. However does not (yet) implement the restriction described in https://github.com/pydata/xarray/issues/9365#issuecomment-2291622577.
• [x] Tests added
• [x] New functions/methods are listed in api.rst
• [x] Type hints passing

cc @shoyer, @flamingbear

[TomNicholas]

Pretty sure the mypy failure in the last commit is unrelated to this PR (which passed mypy before today) - see https://github.com/pydata/xarray/pull/9618#issuecomment-2411054245.

[kmuehlbauer]

@TomNicholas https://github.com/pydata/xarray/pull/9621 for the mypy issue

[headtr1ck]

@TomNicholas this should definitely go into whats-new!

[TomNicholas]

this should definitely go into whats-new!

Generally with the datatree stuff we have been taking the approach that since the previous versions of xarray never had DataTree publicly available, that "what's new" isn't really appropriate for all the internal work going on. Instead we're just going to have one what's new entry announcing the new class, and summarise the important changes relative to the old version of datatree in the other repository in a dedicated migration guide.