Back again :). It looks like my cookies are working for verify_session but not for refreshing my token. My cookie (omitting sAccessToken sense it doesn't seem to be necessary):

sIdRefreshToken=c6f406e1-ade3-4db7-97d6-c735fb0bbc52; Path=/; HttpOnly; Expires=Thu, 30 Sep 2032 07:57:47 GMT;sRefreshToken=QyfeadYTj87m%2By%2BuXJl27Eg3FQan%2BQog174P9J5EcvIMT0Et%2B5YbZ9PRnq3PCE3MSgVqVQnDqyIHGVQ5sU/3%2B%2Bgls8jhyqfhxyh2y6P95qC1ovBwu20z8J8FozZZmkfQkb6uYwAbFMWCV1WY79GSGK%2BglQtsnqo1Kx0hamCyHtJYZvQOnsI6CYBqZieHEJlEhzdn39allN8sKwduhqRgxxW%2BASjXs%2B0uUDmfuon24JZ38Cmr9RUgpaBQoKZCwixyf2SZnuM4Q/BoNPC0OFenRIWehZpmI4DMSLJh%2B4YgnKH%2B2gio3alGb5bL/d9K5NR5cs8mpf61CH4tlf1yeBjz3o0L91G9jOGpXl5P%2BMEvWldqEm2Bu662DB6oOoBQNELkcgrAKzUqp9gndOse.20504c65d4352c3d7ebceb956dd59b8c71aa58835180fa65cb8af730b2103504.V2; Expires=Thu, 30 Sep 2032 07:57:47 GMT; HttpOnly; Path=/api/auth/session/refresh;