It is unlikely, that you can resolve an address by using OSRM backend, because its main functions are routing or map matching.
You should use a geocoder instead, like in the demo below:

'use strict';
var myMap = L.map('mapId').setView([21.0278, 105.8342], 13);
L.tileLayer('https://{s}.tile.openstreetmap.org/{z}/{x}/{y}.png', {
attribution: '© <a href="https://www.openstreetmap.org/">OpenStreetMap</a> contributors'
}).addTo(myMap);
var search = new GeoSearch.GeoSearchControl({
provider: new GeoSearch.OpenStreetMapProvider(),
style: 'bar',
showPopup: true,
popupFormat: ({
query,
result
}) => result.label +
', longitude: ' + parseFloat(result.x).toFixed(6) +
', latitude: ' + parseFloat(result.y).toFixed(6)
});
myMap.addControl(search);
html, body {
margin: 0;
padding: 0;
}
#mapId {
position: absolute;
width: 100%;
height: 100%;
}
<link type="text/css" rel="stylesheet" href="https://cdn.jsdelivr.net/npm/leaflet@1/dist/leaflet.min.css">
<script src="https://cdn.jsdelivr.net/npm/leaflet@1/dist/leaflet-src.min.js"></script>
<script src="https://cdn.jsdelivr.net/npm/leaflet-geosearch@3/dist/bundle.min.js"></script>
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/leaflet-geosearch@3/dist/geosearch.min.css">
<div id="mapId"></div>