Fix duplicate /api/auth/member call and add request deduplication

Remove redundant checkMemberStatus() from coming-soon page since the
auth-init plugin already handles it. Add in-flight request deduplication
to prevent concurrent calls from any source. Strip debug console.logs.

app/pages/coming-soon.vue

@@ -91,8 +91,6 @@ const loginError = ref("");
 
 const isFormValid = computed(() => email.value && email.value.includes("@"));
 
-await checkMemberStatus();
-
 const handleLogin = async () => {
   if (isLoggingIn.value) return;