Edit in JSFiddle 
<!-- Replace <YOUR_API_ACCESS_TOKEN> with your LocationIQ token before using this code. -->
<!DOCTYPE html>
<html>
    <head>
        <meta charset='utf-8' />
        <title>Draw Polygons</title>
        <meta name='viewport' content='initial-scale=1,maximum-scale=1,user-scalable=no' />
        
        <script src='https://tiles.locationiq.com/v3/libs/maplibre-gl/5.24.0/maplibre-gl.js?v=0.1.9'></script>
        <link href='https://tiles.locationiq.com/v3/libs/maplibre-gl/5.24.0/maplibre-gl.css?v=0.1.9' rel='stylesheet' />
        
        <script src='https://tiles.locationiq.com/v3/libs/liq/liq-styles-ctrl-libre-gl-v5.js?v=0.1.9'></script>
        <link href='https://tiles.locationiq.com/v3/css/liq-styles-ctrl-libre-gl.css?v=0.1.9' rel="stylesheet" />
        
        <!-- 
            You need to include the mapbox-gl draw plugin to have interactive drawing controls
        -->
        
        <script src="https://www.unpkg.com/@mapbox/[email protected]/dist/mapbox-gl-draw.js"></script>
        <link
            rel="stylesheet"
            href="https://www.unpkg.com/@mapbox/[email protected]/dist/mapbox-gl-draw.css"
        />

        <style>
            body { margin:0px; padding:0px; }
            #map { position:absolute; top:0px; bottom:0px; width:100%; }
        </style>
    </head>
    
    <body>
        <div id='map'></div>
        <script>

            MapboxDraw.constants.classes.CANVAS = 'maplibregl-canvas';
            MapboxDraw.constants.classes.CONTROL_BASE = 'maplibregl-ctrl';
            MapboxDraw.constants.classes.CONTROL_PREFIX = 'maplibregl-ctrl-';
            MapboxDraw.constants.classes.CONTROL_GROUP = 'maplibregl-ctrl-group';
            MapboxDraw.constants.classes.ATTRIBUTION = 'maplibregl-ctrl-attrib';
            
            //Add your LocationIQ Access Token here - https://my.locationiq.com/
            locationiq.key = '<YOUR_API_ACCESS_TOKEN>';
            //Define the map and configure the map's theme
            var map = new maplibregl.Map({
                container: 'map',
                style: locationiq.getLayer("Streets"),
                zoom: 12,
                center: [-122.42, 37.779]
            });

            //Add draw controls
            var draw = new MapboxDraw({
               displayControlsDefault: false,
               controls: {
                   polygon: true,
                   trash: true
               }
            });
           
            map.addControl(draw);

            //Add listeners
            map.on('draw.create', updateArea);
            map.on('draw.delete', updateArea);
            map.on('draw.update', updateArea);

            //This function is called when a draw event is triggered (create, delete, update)
            //API ref for all that you can do with the draw control: https://github.com/mapbox/mapbox-gl-draw/blob/master/docs/API.md
            function updateArea(e) {
                var data = draw.getAll();
                //We are simply logging all the geometries into console
                //Your first shape's points data can be found in features->0->geometry->coordinates
                console.log(data);
                //You can use http://turfjs.org/ to get bounding boxes, area, etc for these shapes
            }

        </script>
    </body>
</html>