How to draw a circle which wraps one of the poles on mercator (EPSG:4326) with Openlayers 7?

Question

I'd like to draw visiblity circles (i.e. solid angle of visibility around a given lat/lon point on a point at a given altitude, projected on the earth surface) and have no problem except when one of the poles is wrapped by the "circle"/projected polygon (in reality, as I use the EPSG:4326 projection, the "circle" is an ellipse with two focal points on the North-South axis, see Tissot's Indicatrix on Wikipedia). In this case (North or south pole is wrapped), the resulting polygon misses a latitude band portion starting from the highest polygon latitude to the 90° latitude (if north pole) or lowest polygon latitude to the -90° latitude (if south pole).

See screenshots below: **- first one: ** what I obtain using Openlayers' ol.geom.Polygon.circular(...) method in the code below:

 const vectorLayer4326 = new ol.layer.Vector({
     source: new ol.source.Vector(),
     style: polygon_style,
 });

 const radius = 7708025;
 let x, y;
 x = 0;
 for (y = 9; y <= 50; y += 10) {
     const circle4326 = ol.geom.Polygon.circular([x, y], radius, 128);
     vectorLayer4326.getSource().addFeature(new ol.Feature(circle4326));
 }

Incorrect visibility circles

**- second one: ** what I expect to get (I obtained it using the almost same code as above, but I added a fixing method. What it does is explained below the code snippet):

 const vectorLayer4326 = new ol.layer.Vector({
     source: new ol.source.Vector(),
     style: polygon_style,
 });

 const radius = 7708025;
 let x, y;
 x = 0;
 for (y = 9; y <= 50; y += 10) {
     const circle4326 = **fix_OL_visi_circle_pole_vertices**(ol.geom.Polygon.circular([x, y], radius, 128));
     vectorLayer4326.getSource().addFeature(new ol.Feature(circle4326));

The fix_OL_visi_circle_pole_vertices(Polygon) method is a fix I did to correct the Polygon geometry by forcibly adding the "corners" ([-180,90], [180, 90] points for North pole and [-180,-90], [180,-90] points for South pole) when detecting a longitude leap. But obviously, I'd rather have a clean solution

Correct visibility circles

And the Openlayers' map initialization: `

const map4326 = new ol.Map({
    layers: [
        tiles_layer,
        vectorLayer4326
    ],
    target: 'map',
    view: new ol.View({
        projection: 'EPSG:4326',
        center: [0, 0],
        zoom: 2,
    }),
});

`

I had the same issue with Leaflet, changed tthe projection to EPSG:3395, which solved the geometric problem, but then I couldn't fix the tiles to match the correct latitudes. Looking in every direction, I tried to change the map display technology for OpenLayers when I saw their Tissot indicatrix example, hoping it would support the pole wrapping case. Unfortunately, it had the same issue than Leaflet. So I analyzed the generated geometry and produced the fix described previously.

But as I am not a geographer, I hope there is a solution based on changing projections/transformations from a different projection than Mercator to the EPSG:4326 I use.

Thanks in advance for any help.