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I Think you can use Arcade to create an expression.

I dont really know what im doing. Just pasted the code from: VxCount = !shape!.pointcount fuction in AGOL.

Function CountVertices(geom) {
    var cnt_vertices = Null;
    var geom_type = TypeOf(geom);
    Console(geom_type);
    if (geom_type == "Point") {
        cnt_vertices = 1;
    } else if (geom_type == "Multipoint") {
        cnt_vertices = Count(geom.points);
    } else if (geom_type == "Polyline") {
        var cnt_line = 0;
        for (var i = 0; i < Count(geom.paths); i++) { 
            cnt_line += Count(geom.paths[i]);
        }
        cnt_vertices = cnt_line;
    } else if (geom_type == "Polygon") {
        var cnt_pol = 0;
        for (var i = 0; i < Count(geom.rings); i++) { 
            cnt_pol += Count(geom.rings[i]);
        }
        cnt_vertices = cnt_pol;
    } else {
        // this should not happen...    
    }
    return cnt_vertices;
}


return CountVertices(Geometry($feature))

Some if statements at the end might solve your problem. Or use modulus to get two symbols, one for even numbers and one for odd.