Props does not gets cleared in inertia ?

In my projects / Index component i have this code and when I search anything and get's the expected result and try to navigate back to the same projects/ index url on i had searched earlier the input search component get's clear and even also from the url params.

my code

const page = usePage();
const projects = computed(() => page.props.projects);

const breadcrumbLinks = [
    { name: 'Dashboard', href: route('admin.dashboard') },
    { name: 'Projects', href: route('projects.index') },
];

// Create form with search field
const form = useForm({
    search: page.props.search ?? ''
});

// Debounced request for search
const debouncedSearch = debounce(() => {
    form.get(route('projects.index'), {
        replace: true,
        preserveScroll: true,
        preserveState: true
    });
}, 500);

// Watch form.search directly
watch(() => form.search, () => {
    debouncedSearch();
});

// Cancel debounce on unmount
onUnmounted(() => {
    debouncedSearch.cancel();
});

The main issue comes here in the Notifications / Index component I was expecting the same behaviour but did not get the input cleared.

1. The url search query gets removed but the input search has the searched value.
2. Event using the smae approach for the both components.

my code

const page = usePage();
const notifications = computed(() => page.props.notifications);

// Form (search + filter + date)
const form = useForm({
    search: page.props.search ?? "",
    filter: page.props.filter ?? "all",
    from_date: page.props.from_date ?? "",
    to_date: page.props.to_date ?? "",
});

// Debounced request
const debouncedSearch = debounce(() => {
    form.get(route("notifications.index"), {
        replace: true,
        preserveScroll: true,
        preserveState: true,
    });
}, 500);

// Watch search, filter, and dates
watch(
    () => [form.search, form.filter, form.from_date, form.to_date],
    () => {
        debouncedSearch();
    }
);

// Cleanup
onUnmounted(() => {
    debouncedSearch.cancel();
});

Is there anything I am missing ?