Close mobile search input on click outside

### Describe the bug

There is no way to close this search input on a subpage.
<img width="409" height="258" alt="Image" src="https://github.com/user-attachments/assets/6733808c-1077-497c-a732-4efb280349fc" />


### Additional context

_No response_

### Logs

```shell-script

```