gdalwarp: Using -dstnodata nan with output format COG is creating .aux.xml file

[maawoo]

Expected behavior and actual behavior.

Expected:
gdalwarp -of COG -co COMPRESS=DEFLATE -srcnodata 0 -dstnodata nan in.tif out.tif
behaves similar to
gdalwarp -of GTiff -co COMPRESS=DEFLATE -srcnodata 0 -dstnodata nan in.tif out.tif

Actual:
Using the COG driver as output format creates an additional .aux.xml file with the following content:

<PAMDataset>
  <PAMRasterBand band="1">
    <Description>Gamma0_VH</Description>
    <NoDataValue le_hex_equiv="000000000000F87F">nan</NoDataValue>
  </PAMRasterBand>
</PAMDataset>

I wasn't able to find much information regarding this. Other than that I don't see any important differences in both files and nan is successfully used as the nodata value in both:

Metadata:
  AREA_OR_POINT=Area
  Band_1=Gamma0_VH
Image Structure Metadata:
  COMPRESSION=DEFLATE
  INTERLEAVE=BAND
  LAYOUT=COG

Band 1 Block=512x512 Type=Float32, ColorInterp=Gray
  Description = Gamma0_VH
  Minimum=0.000, Maximum=4321.163, Mean=0.060, StdDev=0.534
  NoData Value=nan
  Overviews: 14574x11382, 7287x5691, 3643x2845, 1821x1422, 910x711, 455x355
  Metadata:
    STATISTICS_MAXIMUM=4321.1630859375
    STATISTICS_MEAN=0.060035507447176
    STATISTICS_MINIMUM=3.781369173339e-08
    STATISTICS_STDDEV=0.53371453663701
    STATISTICS_VALID_PERCENT=63.98

Metadata:
  AREA_OR_POINT=Area
  Band_1=Gamma0_VH
Image Structure Metadata:
  COMPRESSION=DEFLATE
  INTERLEAVE=BAND

Band 1 Block=29148x1 Type=Float32, ColorInterp=Gray
  Description = Gamma0_VH
  Minimum=0.000, Maximum=4321.163, Mean=0.060, StdDev=0.534
  NoData Value=nan
  Metadata:
    STATISTICS_MAXIMUM=4321.1630859375
    STATISTICS_MEAN=0.060035507447113
    STATISTICS_MINIMUM=3.781369173339e-08
    STATISTICS_STDDEV=0.53371453663706
    STATISTICS_VALID_PERCENT=63.98

Steps to reproduce the problem.

See above

Operating system

Windows 10

GDAL version and provenance

GDAL 3.3.1 via conda