DataArray.transpose with transpose_coords=True does not change coords order

What happened?

I used DataArray.transpose with transpose_coords=True to change the coords order from
startings_dims = "dim_0", "dim_1", "dim_2"
to
reordered_dims = "dim_2", "dim_1", "dim_0".

The order of dims was correctly transposed but the order of coords remained unchanged.

What did you expect to happen?

I expected the transposed coords to be in the new order:

reordered_dims = "dim_2", "dim_1", "dim_0"

Minimal Complete Verifiable Example

import numpy as np
import pandas as pd
import xarray as xr

np.random.seed(0)
temperature = np.random.randn(4, 4, 3)
dim_0_values = [1, 2, 3, 4]
dim_1_values = [5, 6, 7, 8]
dim_2_values = pd.date_range("2014-09-06", periods=3)
starting_dims = "dim_0", "dim_1", "dim_2"

da = xr.DataArray(
    data=temperature,
    dims=starting_dims,
    coords=dict(
        dim_0=dim_0_values,
        dim_1=dim_1_values,
        dim_2=dim_2_values,
    ),
    attrs=dict(
        description="Ambient temperature.",
        units="degC",
    ),
)

print(f"{da.dims=}")
print(f"{da.coords.keys()=}")

reordered_dims = "dim_2", "dim_1", "dim_0"
print(f"{da.transpose(*reordered_dims).dims=}")
print(f"{da.transpose(*reordered_dims).coords.keys()=}")
print(f"{da.transpose(*reordered_dims, transpose_coords=True).coords.keys()=}")

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.

Relevant log output

da.dims=('dim_0', 'dim_1', 'dim_2')
da.coords.keys()=KeysView(Coordinates:
  * dim_0    (dim_0) int32 1 2 3 4
  * dim_1    (dim_1) int32 5 6 7 8
  * dim_2    (dim_2) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08)
da.transpose(*reordered_dims).dims=('dim_2', 'dim_1', 'dim_0')
da.transpose(*reordered_dims).coords.keys()=KeysView(Coordinates:
  * dim_0    (dim_0) int32 1 2 3 4
  * dim_1    (dim_1) int32 5 6 7 8
  * dim_2    (dim_2) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08)
da.transpose(*reordered_dims, transpose_coords=True).coords.keys()=KeysView(Coordinates:
  * dim_0    (dim_0) int32 1 2 3 4
  * dim_1    (dim_1) int32 5 6 7 8
  * dim_2    (dim_2) datetime64[ns] 2014-09-06 2014-09-07 2014-09-08)

Anything else we need to know?

No response

Environment

Start by reproducing the reported behavior with the DataArray.transpose entry point and the provided minimal example. Read the transpose_coords behavior in the linked DataArray.transpose documentation and implementation, then verify that the coordinate key order matches the requested dimension order when the issue is fixed.