refactor: add search in appState type

[tolluset]

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Add search property to AppState type

Explicitly adding the search property to AppState type to improve TypeScript support. This property is commonly used in authentication flows to preserve query parameters during redirects, but was missing from the type definition.

e.g.) appState: {search: '?invitation_id=xxxxxxxx-xxxx-xxxx-xxxx-xxxxxxxxxxxx', returnTo: '/invitation/signin'}

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