Choose search page version with URL argument

### Have you read the Contributing Guidelines on issues?

- [X] I have read the [Contributing Guidelines on issues](https://github.com/facebook/docusaurus/blob/main/CONTRIBUTING.md#issues).

### Description

It would be very useful to be able to pre-select version number for the search page with a URL argument.

### Has this been requested on Canny?

Not that I found

### Motivation

This feature would allow embedding the search page on other tools (website, IDE, else) by pointing directly to the wanted page.

In my use-case, developing an IDE with a custom programming language, it would allow me to have the documentation and an open search box with the wanted version already pre-selected for a smoother UX

### API design

As it's simply a feature, it could be just enabled by default and not require any particular configuration.

### Have you tried building it?

I simply gathered GET arguments from the URL and try to match it with one element from the list of available version. The URL looks something like this `https://gama-platform.org/search?version=1.9.2`

### Self-service

- [ ] I'd be willing to contribute this feature to Docusaurus myself.