feat: add UI conformance and launch context

webui/src/styles/auth-gate.css

@@ -49,7 +49,7 @@
 
 .public-card h1 {
   margin: 0;
-  max-width: 620px;
+  max-width: 680px;
   font-size: clamp(30px, 4vw, 46px);
   line-height: 1.08;
   color: var(--text-strong);
@@ -115,7 +115,7 @@
   font-weight: 700;
   padding: 8px 10px;
   margin: -8px -10px;
-  border-radius: 7px;
+  border-radius: var(--radius-md);
   cursor: pointer;
   transition: background-color .12s ease, color .12s ease, box-shadow .12s ease;
 }
@@ -125,7 +125,7 @@
 .account-pill {
   padding: 8px 10px;
   margin: 0;
-  border-radius: 7px;
+  border-radius: var(--radius-md);
   transition: background-color .12s ease, color .12s ease, box-shadow .12s ease;
   cursor: pointer;
 }
@@ -145,7 +145,7 @@
 }
 
 .dropdown-item {
-  border-radius: 6px;
+  border-radius: var(--radius-compact);
   transition: background-color .12s ease, color .12s ease;
 }