JSFiddle - React, Tailwind, and code Playground

HTML

<span id="count"></span>
<select id="combobox" style="">
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
    <option value="0">Tous</option><option value="10837">Aucun libellé (ID: 10837)</option>
   ...

CSS

.custom-combobox {
    position: relative;
    display: inline-block;
  }
  .custom-combobox-toggle {
    position: absolute;
    top: 0;
    bottom: 0;
    margin-left: -1px;
    padding: 0;
    /* support: IE7 */
    *height: 1.7em;
    *top: 0.1em;
  }
  .custom-combobox-input {
    margin: 0;
    padding: 0.3em;
  }

JavaScript

(function( $ ) {
    $.widget( "custom.combobox", {
      _create: function() {
        this.wrapper = $( "<span>" )
          .addClass( "custom-combobox" )
          .insertAfter( this.element );
 
        this.element.hide();
        this._createAutocomplete();
        this._createShowAllButton();
      },
 
      _createAutocomplete: function() {
        var selected = this.element.children( ":selected" ),
          value = selected.val() ? selected.text() : "";
 
        this.input = $( "<input>" )
          .appendTo( this.wrapper )
          .val( value )
          .attr( "title", "" )
          .addClass( "custom-combobox-input ui-widget ui-widget-content ui-state-default ui-corner-left" )
          .autocomplete({
            delay: 0,
            minLength: 0,
            source: $.proxy( this, "_source" )
          })
          .tooltip({
            tooltipClass: "ui-state-highlight"
          });
 
        this._on( this.input, {
          autocompleteselect: function( event, ui ) {
            ui.item.option.selected = true;
            this._trigger( "select", event, {
              item: ui.item.option
            });
          },
 
          autocompletechange: "_removeIfInvalid"
        });
      },
 
      _createShowAllButton: function() {
        var input = this.input,
          wasOpen = false;
 
        $( "<a>" )
          .attr( "tabIndex", -1 )
          .attr( "title", "Show All Items" )
          .tooltip()
          .appendTo( this.wrapper )
          .button({
            icons: {
              primary: "ui-icon-triangle-1-s"
            },
            text: false
          })
          .removeClass( "ui-corner-all" )
          .addClass( "custom-combobox-toggle ui-corner-right" )
          .mousedown(function() {
            wasOpen = input.autocomplete( "widget" ).is( ":visible" );
          })
          .click(function() {
            input.focus();
 
            // Close if already visible
            if ( wasOpen ) {
          ...