InertiaJS router.get request with params not preserving state: always full refreshing page

[andcl]

In the docs, we can find:

State preservation

...
You can instruct Inertia to preserve the component's state when using the get method by setting the preserveState option to true.

router.get('/users', { search: 'John' }, { preserveState: true })

...

I use this in my React application precisely for searching & filtering rows in, for example, a datatable.

For that, I have binded that search string to a text input content, so changing it launches a GET request that, in turn, changes the URL, e.g. http://localhost/example?search=Johnny. And because of that URL change, Inertia then always triggers a full page reload, making preserveState: true option totally useless in my case...

How is the "search functionality" supposed to be implemented then? What am I failing at?

Thanks in advance.