Getting GML features with OpenLayers from Spanish Cadaster fails

Question

I'm trying to paint parcels retrieved from Spanish land register by their API (as described here, PDF Spanish only!). It's an WFS service (complying INSPIRE) and offers the information as GML versión 3.2.1 files.

Here an example response (using this call) to retrieve parcels by their cadaster reference:

<?xml version="1.0" encoding="ISO-8859-1"?>
<!--Parcela Catastral de la D.G. del Catastro.-->
<!--La precisión es la que corresponde nominalmente a la escala de captura de la cartografía-->
<FeatureCollection xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:gml="http://www.opengis.net/gml/3.2" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cp="http://inspire.ec.europa.eu/schemas/cp/4.0" xmlns:gmd="http://www.isotc211.org/2005/gmd" xsi:schemaLocation="http://www.opengis.net/wfs/2.0 http://schemas.opengis.net/wfs/2.0/wfs.xsd http://inspire.ec.europa.eu/schemas/cp/4.0 http://inspire.ec.europa.eu/schemas/cp/4.0/CadastralParcels.xsd" xmlns="http://www.opengis.net/wfs/2.0" timeStamp="2022-08-30T19:29:52" numberMatched="1" numberReturned="1">
  <member>
    <cp:CadastralParcel gml:id="ES.SDGC.CP.3662001TF3136S">
      <cp:areaValue uom="m2">3814</cp:areaValue>
      <cp:beginLifespanVersion>2021-06-09T00:00:00</cp:beginLifespanVersion>
      <cp:endLifespanVersion xsi:nil="true" nilReason="http://inspire.ec.europa.eu/codelist/VoidReasonValue/Unpopulated"></cp:endLifespanVersion>
      <cp:geometry>
        <gml:MultiSurface gml:id="MultiSurface_ES.SDGC.CP.3662001TF3136S" srsName="http://www.opengis.net/def/crs/EPSG/0/25830">
          <gml:surfaceMember>
            <gml:Surface gml:id="Surface_ES.SDGC.CP.3662001TF3136S.1" srsName="http://www.opengis.net/def/crs/EPSG/0/25830">
              <gml:patches>
                <gml:PolygonPatch>
                <gml:exterior>
                    <gml:LinearRing>
                      <gml:posList srsDimension="2" count="68">233565.81 4016077.37 233581.88 4016079.67 233582.39 4016079.64 233582.41 4016079.64 233582.93 4016079.61 233582.95 4016079.79 233584.21 4016095.89 233590.37 4016086.81 233608.95 4016076.64 233622.4 4016059.04 233634.4 4016039.96 233635.42 4016038.33 233637.7 4016034.42 233639.69 4016030.68 233639.92 4016030.24 233641.36 4016028.14 233641.81 4016027.47 233643.7 4016024.87 233644.86 4016023.27 233646.95 4016020.39 233645.01 4016006.5 233655.45 4015995.96 233655.14 4015995.64 233651.48 4015991.83 233650.44 4015990.75 233648.45 4015992.4 233640.59 4015999.13 233639.85 4015999.81 233639.12 4016000.48 233637.69 4016001.88 233636.31 4016003.33 233634.97 4016004.81 233633.68 4016006.34 233633.17 4016006.97 233628.43 4016014.77 233626.25 4016018.35 233623.19 4016023.38 233623.04 4016023.63 233619.94 4016026.88 233615.37 4016031.67 233614.08 4016033.01 233613.46 4016033.66 233610.82 4016035.98 233602.71 4016043.12 233600.17 4016045.28 233596.47 4016048.66 233591.23 4016053.38 233589.87 4016052.05 233584.62 4016052.25 233584.33 4016052.26 233581.97 4016049.04 233578.37 4016045.27 233576.52 4016043.93 233574.11 4016042.19 233569.38 4016039.9 233564.32 4016038.46 233559.09 4016037.93 233553.84 4016038.31 233548.39 4016039.75 233543.94 4016041.75 233537.63 4016037.54 233535.81 4016033.81 233535.16 4016033.58 233530.41 4016023.48 233532.15 4016035.61 233543.76 4016066.93 233552.15 4016070.9 233565.81 4016077.37</gml:posList>
                    </gml:LinearRing>
                </gml:exterior>
                </gml:PolygonPatch>
              </gml:patches>
            </gml:Surface>
          </gml:surfaceMember>
        </gml:MultiSurface>
      </cp:geometry>
      <cp:inspireId>
        <Identifier xmlns="http://inspire.ec.europa.eu/schemas/base/3.3">
          <localId>3662001TF3136S</localId>
          <namespace>ES.SDGC.CP</namespace>
        </Identifier>
      </cp:inspireId>
      <cp:label>01</cp:label>
      <cp:nationalCadastralReference>3662001TF3136S</cp:nationalCadastralReference>
      <cp:referencePoint>
        <gml:Point gml:id="ReferencePoint_ES.SDGC.CP.3662001TF3136S" srsName="http://www.opengis.net/def/crs/EPSG/0/25830"> 
          <gml:pos>233584.35 4016065.6</gml:pos>
        </gml:Point>
      </cp:referencePoint>
    </cp:CadastralParcel>
  </member>
</FeatureCollection>

Right now I manually parse the XML file and make a vector feature, but would be more elegant to make the feature from GML32 format. To do so, I tried to get the parcel geometry from GML, but without success:

const parser = new ol.format.GML32({
    featureNS: 'http://inspire.ec.europa.eu/schemas/cp',
    featureType: 'CadastralParcel'
});
console.log(parser.readFeature(wfsCPxml));

I also tried using WFS format, but same null result (after changing manually surfaceMember to featureMember as mentioned here):

const wfs = new ol.format.WFS({
  gmlFormat: new ol.format.GML32({
    featureNS: 'http://inspire.ec.europa.eu/schemas/cp',
    featureType: 'CadastralParcel'
  })
});
console.log(parser.readFeature(wfsCPfeaturexml));

Here is the related jsfiddle, any idea what I'm doing wrong?