Utilizza font-awesome con una classe css.
codice HTML:
<!DOCTYPE html>
<html lang="it">
<head>
<meta charset="UTF-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.13.0/css/all.min.css">
<title>Document</title>
<style>
.search-icon {
position: relative;
left: -24px;
padding: 3px;
background: white;
border: 0;
color: gray;
cursor: pointer;
}
</style>
</head>
<body>
<form action="https://hard-questions.com/ricerca" method="POST">
<input type="text" id="s" name="search" placeholder="Cerca nel sito...">
<button type="submit" class="fas fa-search search-icon"></button>
</form>
</body>
</html>