DataArray with multiple (Pandas)Indexes on the same dimension is impossible to align #8236

What happened?

I have a DataArray with a single dimension and multiple (Pandas)Indexes assigned to various coordinates for efficient indexing using sel.

Edit: the problem is even worse than originally described below: such a DataArray breaks all alignment and it's basically unusable...

When I try to add an additional coordinate without any index (I simply use the tuple[dimension, values] way) I get a ValueError about aligning with conflicting indexes.

If the original DataArray only has a single (Pandas)Index everything works as expected.

What did you expect to happen?

I expected that I can simply assign new coordinates without an index.

Minimal Complete Verifiable Example

import xarray as xr

da = xr.DataArray(
    [1, 2, 3],
    dims="t",
    coords={
        "a": ("t", [3, 4, 5]),
        "b": ("t", [5, 6, 7])
    }
)

# set one index
da2 = da.set_xindex("a")

# set second index (same dimension, maybe thats a problem?)
da3 = da2.set_xindex("b")

# this works
da2.coords["c"] = ("t", [2, 3, 4])

# this does not
da3.coords["c"] = ("t", [2, 3, 4])

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

ValueError: cannot re-index or align objects with conflicting indexes found for the following dimensions: 't' (2 conflicting indexes)
Conflicting indexes may occur when

• they relate to different sets of coordinate and/or dimension names
• they don't have the same type
• they may be used to reindex data along common dimensions

Anything else we need to know?

No response

Environment

I have not yet tried this with a newer version of xarray....