use zod schemes for validation

src/routes/admin/logout/+server.ts

@@ -1,5 +1,6 @@
 import type { RequestHandler } from '@sveltejs/kit';
 import { deleteSession, getSession, sessionCookieName } from '$lib/server/session';
+import { env as publicEnv } from '$env/dynamic/public';
 
 export const POST = (async ({ cookies }) => {
 	if (getSession(cookies) == null) {
@@ -9,7 +10,7 @@ export const POST = (async ({ cookies }) => {
 	}
 
 	deleteSession(cookies);
-	cookies.delete(sessionCookieName);
+	cookies.delete(sessionCookieName, { path: `${publicEnv.PUBLIC_BASE_PATH}/admin` });
 
 	return new Response();
 }) satisfies RequestHandler;