feat: enable site search, fix splits tier claim and rate limit example

- Enable Pagefind search via Nextra search config and Search component
- Fix splits doc: was "Pro tier or higher required" but API has no tier gate
- Fix pricing page: rate limit reset example was 13-digit (ms), API returns 10-digit (seconds)

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

Author: Mlaz-code

app/[lang]/layout.tsx

@@ -1,5 +1,5 @@
 import { Footer, Layout, Navbar } from 'nextra-theme-docs'
-import { Head } from 'nextra/components'
+import { Head, Search } from 'nextra/components'
 import { getPageMap } from 'nextra/page-map'
 import Link from 'next/link'
 import { PostHogProvider } from '../../components/PostHogProvider'
@@ -56,6 +56,7 @@ export default async function LangLayout({ children, params }) {
         <PostHogProvider>
           <Layout
             pageMap={await getPageMap(`/${lang}`)}
+            search={<Search />}
             sidebar={{ defaultMenuCollapseLevel: 1, toggleButton: true }}
             toc={{ backToTop: true }}
             feedback={{ content: null }}

content/en/api-reference/splits.mdx

@@ -14,7 +14,7 @@ GET /api/v1/splits
 
 ## Authentication
 
-Requires API key. **Pro tier or higher required.** Your account must have the `splits` feature enabled.
+Requires API key. Available on all tiers.
 
 ## What are betting splits?
 

content/en/pricing.mdx

@@ -133,7 +133,7 @@ All API requests are rate limited per API key. Rate limit headers are included i
 ```
 X-RateLimit-Limit: 300
 X-RateLimit-Remaining: 299
-X-RateLimit-Reset: 1703123456789
+X-RateLimit-Reset: 1703123460
 ```
 
 ### Rate Limit Response

next.config.mjs

@@ -2,6 +2,7 @@ import nextra from 'nextra';
 
 const withNextra = nextra({
   defaultShowCopyCode: true,
+  search: { codeblocks: false },
 });
 
 export default withNextra({