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
1454832041,I_kwDOAMm_X85Wtvmp,7297,stack().unstack() not the same as original for datavars dependent on single coordinate of multi_index,96822049,open,0,,,6,2022-11-18T10:12:52Z,2023-01-17T18:28:44Z,,NONE,,,,"### What is your issue?
(See MVCE example) 
The combination `ds.stack().unstack()` doesn't entirely give back the original ds, when there's a datavariable that only depends on a subset of coords of the multi-index used for stacking.

1. Is this on purpose? And if so, what's the rationale?
2. I would imagine that it could also be more memory efficient, when the original indexes `x` and `y` are kept that make up the multi-index `(midx=[x,y])` after a `stack()` operation. Because then you don't have to express and thus repeat the values of dataarrays that only depend on a subset of the indexes that make up the multi-index.

### MVCE
```
# xarray==2022.11.0
import xarray as xr

ds = xr.Dataset(coords={'x':[1,2], 'y':[3,4]})
ds['a'] = ds.x + 5
# <xarray.Dataset>
# Dimensions:  (x: 2, y: 2)
# Coordinates:
#   * x        (x) int32 1 2
#   * y        (y) int32 3 4
# Data variables:
#     a        (x) int32 6 7

ds_stacked = ds.stack(midx=['x','y'])
# <xarray.Dataset>
# Dimensions:  (midx: 4)
# Coordinates:
#   * midx     (midx) object MultiIndex
#   * x        (midx) int32 1 1 2 2
#   * y        (midx) int32 3 4 3 4
# Data variables:
#     a        (midx) int32 6 6 7 7

ds_unstacked = ds_stacked.unstack()
# <xarray.Dataset>
# Dimensions:  (x: 2, y: 2)
# Coordinates:
#   * x        (x) int32 1 2
#   * y        (y) int32 3 4
# Data variables:
#     a        (x, y) int32 6 6 7 7
```

### Expected
`ds_unstacked` to be the same as `ds`. 
Instead the variable `a` has now also become a function of coordinate `y`, but that's not entirely correct.
I.e., after `ds.stack()`, that the variable 'a' is still only dependent on the original coordinate 'x', which is just a part of the multi-index.

```
ds_stacked = ds.stack(midx=['x','y'])
# <xarray.Dataset>
# Dimensions:  (midx: 4)
# Coordinates:
#   * midx     (midx) object MultiIndex
#   * x        (midx) int32 1 1 2 2
#   * y        (midx) int32 3 4 3 4
# Data variables:
#     a        (x) int32 6 6 7 7
```
**Maybe for clarity**
```
# <xarray.Dataset>
# Dimensions:  (midx: 4)
# Coordinates:
#   * midx     (midx) object MultiIndex
#   * x        (midx) int32 1 1 2 2
#   * y        (midx) int32 3 4 3 4
# Data variables:
#     a        (midx.x) int32 6 6 7 7
```
**Or maybe to save memory**
Make a relation/difference between midx.x (repeated values of x due to stacking) and x (original unique values).
```
# <xarray.Dataset>
# Dimensions:  (midx: 4)
# Coordinates:
#   * midx     (midx) object MultiIndex
#   * x        (midx) int32 1 1 2 2
#   * y        (midx) int32 3 4 3 4
# Data variables:
#     a        (x) int32 6 7
```","{""url"": ""https://api.github.com/repos/pydata/xarray/issues/7297/reactions"", ""total_count"": 1, ""+1"": 1, ""-1"": 0, ""laugh"": 0, ""hooray"": 0, ""confused"": 0, ""heart"": 0, ""rocket"": 0, ""eyes"": 0}",,,13221727,issue