Composite operations on chunked array types not dispatched through chunk manager

What happened?

The arkouda-xarray chunk manager (found here) is designed to allow Arkouda's distributed arrays to operate as chunked arrays in XArray. (Note Arkouda's array's also implement the array API, which was being used for XArray interoperability before the chunk manager was created).

When executing various operations on XArray DataArrays or DataSets that are backed by the Arkouda chunk manager, I noticed that they are not being routed through the chunk manager itself. For example, calling myArkoudaBackedArray.mean(axis="some-axis") does not get routed through ArkoudaManager.reduction. However, the operation is successful and produces the correct result, indicating that the array-api implementation of mean is being used instead (i.e., the arkouda-backed array is being treated as a duck array).

https://github.com/jeremiah-corrado/arkouda-xarray-seasonal-avgs-example/blob/main/README.md contains a full example where I observed the above behavior. It includes instructions to get Arkouda set up for XArray interoperability.

pinging @TomNicholas, since we discussed this the other day.

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.

Relevant log output

No response

Anything else we need to know?

No response

Environment

Start with arkouda_xarray/arkoudamanager.py and the linked Arkouda seasonal-avgs example; reproduce mean(axis=...) on an Xarray object backed by the chunk manager. Trace why the call bypasses ArkoudaManager.reduction and instead uses the array-API path. Done when composite operations are routed through the chunk manager and the behavior is covered by regression tests.