Calculating tangents for the mesh

I want to calculate tangent vectors for the mesh. I can’t call Unity’s default RecalculateTangents method because I need to invoke it from a non-main thread.

I have found the code for calculating:

public static void RecalculateTangents(Mesh mesh)
{
    int[] triangles = mesh.triangles;
    Vector3[] vertices = mesh.vertices;
    Vector2[] uv = mesh.uv;
    Vector3[] normals = mesh.normals;
    
    int triangleCount = triangles.Length;
    int vertexCount = vertices.Length;

    Vector3[] tan1 = new Vector3[vertexCount];
    Vector3[] tan2 = new Vector3[vertexCount];

    Vector4[] tangents = new Vector4[vertexCount];

    for (int a = 0; a < triangleCount; a += 3)
    {
        int i1 = triangles[a + 0];
        int i2 = triangles[a + 1];
        int i3 = triangles[a + 2];

        Vector3 v1 = vertices[i1];
        Vector3 v2 = vertices[i2];
        Vector3 v3 = vertices[i3];

        Vector2 w1 = uv[i1];
        Vector2 w2 = uv[i2];
        Vector2 w3 = uv[i3];

        float x1 = v2.x - v1.x;
        float x2 = v3.x - v1.x;
        float y1 = v2.y - v1.y;
        float y2 = v3.y - v1.y;
        float z1 = v2.z - v1.z;
        float z2 = v3.z - v1.z;

        float s1 = w2.x - w1.x;
        float s2 = w3.x - w1.x;
        float t1 = w2.y - w1.y;
        float t2 = w3.y - w1.y;
        
        float div = s1 * t2 - s2 * t1;
        float r = div == 0.0f ? 0.0f : 1.0f / div;

        Vector3 sDir = new Vector3((t2 * x1 - t1 * x2) * r, (t2 * y1 - t1 * y2) * r, (t2 * z1 - t1 * z2) * r);
        Vector3 tDir = new Vector3((s1 * x2 - s2 * x1) * r, (s1 * y2 - s2 * y1) * r, (s1 * z2 - s2 * z1) * r);

        tan1[i1] += sDir;
        tan1[i2] += sDir;
        tan1[i3] += sDir;

        tan2[i1] += tDir;
        tan2[i2] += tDir;
        tan2[i3] += tDir;
    }
    
    for (int a = 0; a < vertexCount; ++a)
    {
        Vector3 n = normals[a];
        Vector3 t = tan1[a];
        
        Vector3.OrthoNormalize(ref n, ref t);
        tangents[a].x = t.x;
        tangents[a].y = t.y;
        tangents[a].z = t.z;

        tangents[a].w = (Vector3.Dot(Vector3.Cross(n, t), tan2[a]) < 0.0f) ? -1.0f : 1.0f;
    }

    mesh.tangents = tangents;
}

The main problem is that my mesh has 4-dimensional UV coordinates (List of Vector4), but the sample code assumes 2-dimensional UV. How can I calculate tangents for the mesh using 4-dimensional UV?