MapboxSearchBox not working in fullscreen mode

[ouvreboite]

When using the MapboxSearchBox and mapboxgl.FullscreenControl(), when in fullscreen the searchbox no longer works: typing in the search box does not open the result list.

mapbox-gl-js version: 3.2.0
browser: chrome 123.0.6312.87

Steps to Trigger Behavior

1. Create a simple map
2. Add the MapboxSearchBox as a control
3. Add the FullscreenControl as a control
4. In non-fullscreen: the search box work as expected (typing a word display the list of possible search result)
5. In fullscreen: the search box does not work (typing a word does nothing)

Link to Demonstration

https://jsfiddle.net/hytcdL9v/2

Expected Behavior

The MapboxSearchBox should present search result in fullscreen (same as in non-fullscreen)

Actual Behavior

The MapboxSearchBox in fullscreen does nothing