[Bug] Template bug: Searchbar cannot render if the page is built from yaml file.

**Describe the bug**
When I use default/modern template, the search bar only renders if the page is built from `.md`. If the page is built from `.yaml` file, this page cannot render the search bar.

**To Reproduce**
Steps to reproduce the behavior:
1. unzip the attachment [TestZip.zip](https://github.com/dotnet/docfx/files/11485230/TestZip.zip)
2. build and run docfx v2
3. You can find all the home pages (built from markdown file) works perfectly, there are both toc filter and search bar
4. But for content page, there is no search bar. (I have enable the searchbar in docfx.json)

**Expected behavior**
There is search bar on docfx
**Screenshots**
There is a searchbar for home page (built from markdown)
There is no searchbar for content page (built from yaml)

**Context (please complete the following information):**

- Browser: [Chrome, Edge]
- Form factor: [Desktop]
- Docfx version: [2.66.2+95d113dca43efe17044f80b056b40789bd6a65db]
- Template: [default]

**Additional context**
[TestZip.zip](https://github.com/dotnet/docfx/files/11485230/TestZip.zip)