concat fails due to StringDtype introduced by pd.Index

What happened?

This used to work (a few releases of xarray and/or pandas ago):

import xarray as xr
import pandas as pd

da = xr.DataArray([0], dims=["dim_a"], coords=dict(dim_a=["a"]))
db = xr.DataArray([0])
# use concat to add a new dimension with coordinate
db2 = xr.concat([db], pd.Index(["b"], name="dim_a"))
xr.concat([da, db2], dim="dim_a")  # this fails

But now fails with TypeError: Cannot interpret '<StringDtype(storage='python', na_value=nan)>' as a data type because the pd.Index apparently introduces a StringDtype coord, while the coord of da has dtype <U1.

Replacing the pd.Index with xr.Variable still works:

import xarray as xr
import pandas as pd

da = xr.DataArray([0], dims=["dim_a"], coords=dict(dim_a=["a"]))
db = xr.DataArray([0])
# use concat to add a new dimension with coordinate
db3 = xr.concat([db], xr.Variable("dim_a", ["b"]))
xr.concat([da, db3], dim="dim_a")  # this succeeds

Not sure what the bug is here: should pd.Index use <Ux or StringDtype by default? Should xarray.DataArray, when initialized with string coordinates, use <Ux or StringDtype by default? Or should concat know how to handle mixed string types?

At least I find this current situation confusing. If this is not a bug, it might perhaps warrant mentioning this difference between pd.Index and xr.Variable in the concat docs?

What did you expect to happen?

No exception

Minimal Complete Verifiable Example

import xarray as xr
import pandas as pd

da = xr.DataArray([0], dims=["dim_a"], coords=dict(dim_a=["a"]))
db = xr.DataArray([0], dims=["dim_b"], coords=dict(dim_b=["b"]))
# use concat to add a new dimension with coordinate
db2 = xr.concat([db], pd.Index(["b"], name="dim_a"))
xr.concat([da, db2], dim="dim_a")  # this fails

Steps to reproduce

No response

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

Anything else we need to know?

No response

Environment

Run the provided minimal example with xarray, pandas, and NumPy, then trace the two xr.concat calls and the coordinate types produced from pd.Index versus xr.Variable. Determine the intended handling of mixed string dtypes, and consider the issue resolved when the example completes without an exception with regression coverage for the reported case.