Detached mode - entered text is present in two places

## Description

## Reproduction

[**Preview →**](https://codesandbox.io/s/dazzling-kare-jh6z5m?file=/app.tsx)

**Steps**

1. Go to the CodeSandbox link.
2. Click on the Autocomplete.
3. Type "Tw".
4. As you can see "Tw" is present in two places -> in the modal and in the button which triggered the modal.

## Expected behavior

In detached mode when we type something into Autocomplete, the entered text should only be visible in the modal, not in the button which triggers modal.

## Environment

- OS: macOS
- Browser: Brave Version 1.57.62 Chromium: 116.0.5845.180 (Official Build) (x86_64)
- Autocomplete version: 1.11.0

Start with the linked CodeSandbox and its app.tsx entry point, then reproduce the issue by opening Autocomplete in detached mode and typing "Tw". Trace where the entered text is rendered in the modal and triggering button; done when it appears only in the modal, with the reproduction confirming the behavior.

Written by the indexing model from the issue text.