Mobile - Detached mode - clicking enter/search/go closes detached mode

## Description

When using the enter key on the mobile keyboard, the modal closes instead of opening the search results page.

## Reproduction

On **mobile**: https://cuelang.org/

**Steps**

1. Go to the hamburger menu, and open it
2. Click on the search bar, this pops up the detached mode
3. Enter some text in the search bar
4. Hit the enter button of your mobile keyboard

Note that the detached mode closes, you are back in the hamburger menu in stead of the search results page.

https://github.com/algolia/autocomplete/assets/122522301/398da7be-17ca-437b-bb89-cd9097d3f2db

## Expected behavior

I expect to end up on the search results page, like when you do when you click one of the items from the autocomplete.

## Environment

- OS: iOS 17.4.1
- Browser: Safari
- Autocomplete version: 1.12.1

Start by reproducing the detached-mode search flow on the CUE website using mobile Safari: open the hamburger menu, enter a query, and press the keyboard's Enter key. Trace the detached mode and search submission behavior; done means Enter, search, or go opens the search results page instead of closing detached mode.

Written by the indexing model from the issue text.