feat: Implement first admin setup guard to lock registration after initial account creation

- Updated the registration flow to check if the first admin account has been created, preventing further public registrations.
- Introduced `is_first_admin_setup_available` function to determine registration availability.
- Modified the `/register` and `/login` pages to redirect based on the setup state.
- Enhanced the user creation process to handle internal admin accounts correctly.
- Added migration script to enforce the new registration rules in the database.
- Refactored chat API to improve message handling and context building.
- Updated dashboard and settings components for better state management.
- Improved error handling and user feedback across various components.

supabase/migrations/0009_lock_registration_after_first_admin.sql

@@ -0,0 +1,39 @@
+-- 0009: Lock public registration after the first self-host admin account
+-- Run after: supabase/migrations/0008_add_project_progress_and_quota.sql
+
+create or replace function public.is_first_admin_setup_available()
+returns boolean
+language sql
+security definer
+set search_path = public
+as $$
+  select not exists (
+    select 1
+    from public.profiles
+    limit 1
+  );
+$$;
+
+revoke all on function public.is_first_admin_setup_available() from public;
+grant execute on function public.is_first_admin_setup_available() to anon;
+grant execute on function public.is_first_admin_setup_available() to authenticated;
+
+create or replace function public.handle_new_user()
+returns trigger
+language plpgsql
+security definer
+set search_path = public
+as $$
+begin
+  if exists (select 1 from public.profiles limit 1)
+    and coalesce(new.raw_app_meta_data->>'internal_created', 'false') <> 'true' then
+    raise exception 'Registration is closed. The first admin account already exists.';
+  end if;
+
+  insert into public.profiles (id, first_name, last_name, avatar_url)
+  values (new.id, '', '', '')
+  on conflict (id) do nothing;
+
+  return new;
+end;
+$$;