How do i log user out from subdomain using devise

hi guys i am trying to build a blog platform like hashnode/substack where user register on root domain and create blog. I am currently using devise and i have set up subdomain routing. My question is that how do i only allow registration and authentication from root domain and also when in subdomain and i click logout i should be taken to root domain.

i did this in my subdomain

 <% if user_signed_in? %>
                      <li>
                        <%= form_tag(destroy_user_session_path, method: :delete, class: "block px-4 py-2 hover:bg-slate-100 dark:hover:bg-slate-600 dark:hover:text-white font-inter text-sm text-slate-600 dark:text-white font-normal") do %>
                          <button type="submit">
                            <iconify-icon icon="heroicons-outline:login" class="relative top-[2px] text-lg ltr:mr-1 rtl:ml-1"></iconify-icon>
                            Log Out
                          </button>
                        <% end %>
                      </li>
                    <% end %>

and it does not work as it only keeps refreshing