feat: initial ui redesign from demo

src/ui/lib/base-path.ts

@@ -0,0 +1,5 @@
+export function getBasePath(): string {
+  const base = import.meta.env.BASE_URL || "/";
+  if (base === "./" || base === "/") return "";
+  return base.endsWith("/") ? base.slice(0, -1) : base;
+}