ds.coords.dims can display dims not present in the coordinate vars

This (on main) looks wrong to me:

In [1]: import xarray as xr

In [2]: ds = xr.Dataset({'a': ('x', [0, 1])})

In [3]: ds
Out[3]: 
<xarray.Dataset> Size: 16B
Dimensions:  (x: 2)
Dimensions without coordinates: x
Data variables:
    a        (x) int64 16B 0 1

In [4]: ds.coords
Out[4]: 
Coordinates:
    *empty*

In [5]: ds.coords.dims
Out[5]: FrozenMappingWarningOnValuesAccess({'x': 2})

I mean the fact no-one has raised this before means it probably isn't of much consequence, but it does seem incorrect / misleading.

Originally posted by @TomNicholas in https://github.com/pydata/xarray/pull/9451#discussion_r1749072922

The issue here being that the DatasetCoordinates object displays a dim with no associated variable.

I'm not sure whether anything about the concept of "virtual coordinate variables" affects this.

(The FrozenMappingWarningOnValuesAccess is just a Mapping, it's only weird due to the ongoing deprecation cycle started in #8500.)

Reproduce the example with an xarray Dataset and inspect the DatasetCoordinates object, especially its dims mapping. Read the surrounding coordinate and virtual-coordinate handling before deciding the expected behavior; done means the displayed dimensions accurately reflect the coordinate variables and existing relevant tests pass.