Avoid local functions in push

[fjetter]

See dask/dask#11576 for the dask sibling

Using local functions is rather expensive to serialize because the function body has to be serialized instead of merely a reference. That's exacerbated if the function is accessing non-local state since that requires the serialization of the entire context that function is referring to. It is therefore always better for performance to define these functions, regardless of how small they are, as global, top-level functions such that pickle works properly.
The same is true for lambdas which have the same problem.

I'm looking into whether we can have automated tests for this (difficult since our and likely your tests suite is using locals all over the place...)

[welcome]

Thank you for opening this pull request! It may take us a few days to respond here, so thank you for being patient.
If you have questions, some answers may be found in our contributing guidelines.

[fjetter]

I think the test failures are unrelated (e.g. https://github.com/pydata/xarray/actions/runs/12170678414/job/33946120091)

[welcome]

Congratulations on completing your first pull request! Welcome to Xarray! We are proud of you, and hope to see you again!