Question about correct use for regridding global datasets

[mgorfer]

I have a question about the regridding of global datasets.
My code so far was built like this:

def regrid_to_lat_lon(
    ds: xr.Dataset,
    target_res_lat: float = 1,
    target_res_lon: float = 1,
) -> xr.Dataset:
    """
    Regrid any grid to a res_lat x res_lon degree lat lon grid.

    Parameters
    ----------
    ds : xr.Dataset
        Input dataset to be regridded.
    target_res_lat : float, optional
        Target resolution in degrees for latitude, by default 1.
    target_res_lon : float, optional
        Target resolution in degrees for longitude, by default 1.

    Returns
    -------
    xr.Dataset
        Regridded dataset.
    """
    ds_out = xe.util.grid_global(target_res_lat, target_res_lon)
    regridder = xe.Regridder(
        ds,
        ds_out,
        "bilinear",
        periodic=True,
    )

    dr_out = regridder(ds, keep_attrs=True)

    dr_out["x"] = dr_out["lon"].isel(y=0).data
    dr_out["y"] = dr_out["lat"].isel(x=0).data
    dr_out = dr_out.drop(["lat", "lon"])
    dr_out = dr_out.rename({"y": "latitude", "x": "longitude"})

    return dr_out

I just realized, when I use ds_out = xe.util.grid_global(target_res_lat, target_res_lon, cf=True), I do not have to use the lower part of my code, where I drop not needed values from my dr_out. The outputs are equal (dr_out_cf.equals(dr_out_notcf) = True) (except for the one coordinate I am asking about below).
I could not find a lot of information about this on the Docs. The search is also not working there for me at the moment.

The only difference is, that ds_out (the grid) and dr_out (the regridded ds) calculated with cf=True contain a coordinate latitude_longitude which is nan.
ds_out:

<xarray.Dataset>
Dimensions:             (lon: 144, bound: 2, lat: 72)
Coordinates:
  * lon                 (lon) float64 -178.8 -176.2 -173.8 ... 173.8 176.2 178.8
  * lat                 (lat) float64 -88.75 -86.25 -83.75 ... 83.75 86.25 88.75
    latitude_longitude  float64 nan
Dimensions without coordinates: bound
Data variables:
    lon_bounds          (lon, bound) float64 -180.0 -177.5 ... 177.5 180.0
    lat_bounds          (lat, bound) float64 -90.0 -87.5 -87.5 ... 87.5 90.0

Is this coordinate required in the output?

And is my new approach the better one for my use case?

And additionally, would it be possible to specify the latitude and longitude names used by xe.util.grid_global? Normally, my latitude and longitude coords have the names latitude_bins and longitude_bins, which does not work with xesmf.