refactor: url management in hotel reservation flow

app/[lang]/(live)/@bookingwidget/hotelreservation/page.tsx

@@ -2,16 +2,17 @@ import { env } from "@/env/server"
 
 import BookingWidget, { preload } from "@/components/BookingWidget"
 
-import type { PageArgs } from "@/types/params"
+import type { BookingWidgetSearchData } from "@/types/components/bookingWidget"
+import type { LangParams, PageArgs } from "@/types/params"
 
 export default async function BookingWidgetPage({
   searchParams,
-}: PageArgs<{}, URLSearchParams>) {
+}: PageArgs<LangParams, BookingWidgetSearchData>) {
   if (!env.ENABLE_BOOKING_WIDGET_HOTELRESERVATION_PATH) {
     return null
   }
 
   preload()
 
-  return <BookingWidget searchParams={searchParams} />
+  return <BookingWidget bookingWidgetSearchParams={searchParams} />
 }