`rolling_exp` loses coords

[max-sixty]

What happened?

We lose the time coord here — Dimensions without coordinates: time:

ds = xr.tutorial.load_dataset("air_temperature")
ds.rolling_exp(time=5).mean()

<xarray.Dataset>
Dimensions:  (lat: 25, time: 2920, lon: 53)
Coordinates:
  * lat      (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0
  * lon      (lon) float32 200.0 202.5 205.0 207.5 ... 322.5 325.0 327.5 330.0
Dimensions without coordinates: time
Data variables:
    air      (time, lat, lon) float32 241.2 242.5 243.5 ... 296.4 296.1 295.7

(I realize I wrote this, I didn't think this used to happen, but either it always did or I didn't write good enough tests... mea culpa)

What did you expect to happen?

We keep the time coords, like we do for normal rolling:

In [2]: ds.rolling(time=5).mean()
Out[2]:
<xarray.Dataset>
Dimensions:  (lat: 25, lon: 53, time: 2920)
Coordinates:
  * lat      (lat) float32 75.0 72.5 70.0 67.5 65.0 ... 25.0 22.5 20.0 17.5 15.0
  * lon      (lon) float32 200.0 202.5 205.0 207.5 ... 322.5 325.0 327.5 330.0
  * time     (time) datetime64[ns] 2013-01-01 ... 2014-12-31T18:00:00

Minimal Complete Verifiable Example

(as above)

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, 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

INSTALLED VERSIONS

commit: None python: 3.9.13 (main, May 24 2022, 21:13:51) [Clang 13.1.6 (clang-1316.0.21.2)] python-bits: 64 OS: Darwin OS-release: 21.6.0 machine: arm64 processor: arm byteorder: little LC_ALL: en_US.UTF-8 LANG: None LOCALE: ('en_US', 'UTF-8') libhdf5: None libnetcdf: None

xarray: 2022.6.0 pandas: 1.4.3 numpy: 1.21.6 scipy: 1.8.1 netCDF4: None pydap: None h5netcdf: None h5py: None Nio: None zarr: 2.12.0 cftime: None nc_time_axis: None PseudoNetCDF: None rasterio: None cfgrib: None iris: None bottleneck: None dask: 2021.12.0 distributed: 2021.12.0 matplotlib: 3.5.1 cartopy: None seaborn: None numbagg: 0.2.1 fsspec: 2021.11.1 cupy: None pint: None sparse: None flox: None numpy_groupies: None setuptools: 62.3.2 pip: 22.1.2 conda: None pytest: 7.1.2 IPython: 8.4.0 sphinx: 4.3.2