id,node_id,number,title,user,state,locked,assignee,milestone,comments,created_at,updated_at,closed_at,author_association,active_lock_reason,draft,pull_request,body,reactions,performed_via_github_app,state_reason,repo,type
1301380358,I_kwDOAMm_X85NkX0G,6775,bug in DataArray.plot.pcolormesh,35001974,closed,0,,,2,2022-07-12T00:23:25Z,2023-03-16T18:55:32Z,2023-03-16T18:55:32Z,NONE,,,,"### What happened?

The below code fails - I believe its because `_infer_interval_breaks` is applied asymmetrically when one coord is string.

### What did you expect to happen?

Success.

### Minimal Complete Verifiable Example

```Python
from xarray import DataArray

x = DataArray(
    [[1, 2, 3], [4, 5, 6]],
    dims=(""a"", ""b""),
    coords={""a"": [1, 2], ""b"": [""a"", ""b"", ""c""]},
)
x.plot(infer_intervals=False)  # succeeds
x.plot()  # TypeError: Dimensions of C (2, 3) are incompatible with X (3) and/or Y (3); see help(pcolormesh)
```


### MVCE confirmation

- [X] Minimal example — the example is as focused as reasonably possible to demonstrate the underlying issue in xarray.
- [X] Complete example — the example is self-contained, including all data and the text of any traceback.
- [X] Verifiable example — the example copy & pastes into an IPython prompt or [Binder notebook](https://mybinder.org/v2/gh/pydata/xarray/main?urlpath=lab/tree/doc/examples/blank_template.ipynb), returning the result.
- [X] New issue — a search of GitHub Issues suggests this is not a duplicate.

### Relevant log output

_No response_

### Anything else we need to know?

_No response_

### Environment

<details>
version 2022.3.0
</details>
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