The content/children script tags of the head (`scripts[].children`) are lost from the HTML after hydration

Which project does this relate to?

Router

Describe the bug

export const Route = createFileRoute('/test')({
  component: RouteComponent,
  head: () => ({
    scripts: [
      {
        async: true,
        src: `https://www.googletagmanager.com/gtag/js?id=ID`,
      },
      {
        // this is missing on hydrated HTML
        children: `window.dataLayer = window.dataLayer || [];
function gtag(){dataLayer.push(arguments);}
gtag('js', new Date());
gtag('config', 'ID');`,
      },
    ],
  }),
});

Children code in scripts (<script>window.dataLayer...</script>) disappears after hydration on first page visit, reappears if navigating first to another page.

Your Example Website or App

https://stackblitz.com/edit/github-zpekad3w-lxs8xvjn?file=src%2Froutes%2Ftest%2Froute.tsx

Steps to Reproduce the Bug or Issue

1. Build the attached StackBlitz site (npm run build)
2. node .output/server/index.mjs
3. navigate to the test page
4. Refresh the page and check the HTML element in the console <script>window.dataLayer...</script> is missing.

Expected behavior

<script>window.dataLayer...</script> should not disappear after hydration

Screenshots or Videos

https://github.com/user-attachments/assets/badce2ce-7cb9-4ab0-a749-844ecb48fa8c

Platform

• Router / Start Version: 1.168.10 / 1.167.16
• OS: Windows (WSL 2)
• Browser: Chrome
• Browser Version: 146.0.7680.178
• Bundler: vite
• Bundler Version: 8.0.3

Additional context

No response

Start with the attached StackBlitz reproduction and src/routes/test/route.tsx, then run npm run build and node .output/server/index.mjs. Reproduce the refresh on the test page and inspect the script element before and after hydration in Chrome. Done means the scripts[].children content remains present in the hydrated HTML on the first visit.