My Update does not work

I propose that you try this solution. In it:

That said, here we go. I hope you can prove it and comment on the result:

<?php

    session_start();
    require 'conexion.php';

    $nombre = $_POST['nombre'];
    $emai   = $_POST['emai'];
    $pass   = $_POST['pass'];
    $tel    = $_POST['tel'];
    $dir    = $_POST['dir'];
    $id     = $_SESSION['usuario']['ID'];

    // Create connection
    $conn = new mysqli($servername, $username, $password, $dbname);

    // Check connection
    if (!$conn) {

        $arrMensaje=array("mensaje"=>"Error: Fallo de conexión");

    }else{

        if (isset($_SESSION['usuario'])) {

            $strSQL = "UPDATE Usuarios SET name=?, email=?, password=?, phone=?, address=? WHERE ID=?";      
            $stmt=$conn->prepare($strSQL);


            if ($stmt){

                $stmt->bind_param("sssssi", $nombre,$emai,$pass,$tel,$dir,$id);

                if ($stmt->execute()) {
                    $intFilas=$stmt->affected_rows;  
                    $arrMensaje=array("mensaje"=>"Actualizado. Filas afectadas: ".$intFilas.PHP_EOL."Sesión: ".$_SESSION['usuario']['name']);

                }else{

                    $arrMensaje=array("mensaje"=>"No se cumplieron los criterios o clave duplicada " . $stmt->error);
                }

            }else{

                $arrMensaje=array("mensaje"=>"Error: La consulta falló No Error: ".$stmt->errno . "Causa: " . $stmt->error);            
                $stmt->close();
            }


        } else {

            $arrMensaje=array("mensaje"=>"No hay sesión de usuario");

        }

        $conn->close();

    }

    echo $arrMensaje["mensaje"];
?>

You would have to pass a user ID per session ... so that the update of your WHERE is governed there (where is your problem)

In what you went through codes, there is no variable "$ email", but "$ emai"

WHERE email='$email'

(--- Approach ---) If I have all my data and email "[email protected]" I want to change to "[email protected]" in your WHERE you will find the email [email protected] to change it to [email protected] and will not search to [email protected] (according to the query you are using, unless your current mail is saved as a session or you pass it through input hydden (which is later to be implemented in a few more lines to control that it is not manipulated before sending it) to php + sql))

<?php

    session_start();
    require conexion.php;

    extract($_POST); // importa a la lista de variables lo que llega por $_POST

    // Create connection
    $conn = new mysqli($servername, $username, $password, $dbname);

    // Check connection
    if ($conn->connect_error) {
        die("Oops: " . $conn->connect_error);
    }

    if (isset($_SESSION['usuario'])) {

        $cambio = "UPDATE Usuarios SET name='$nombre', email='$emai', password='$pass', phone='$tel', address='$dir' WHERE ID='$id'";        

        if (($conn->query($cambio))) 
        {
            echo $_SESSION['usuario']['name'];
        } else {
            echo "Error: ";
        }

    } else {

        echo"oops";

    }

    $conn->close();

?>

Anyway, since I can not see the file conexion.php, it is impossible to find out if the connection is well made ...

I hope I helped you something.

Greetings

Another error apart those that have been modified by the comments is in the next step:

if (($result=$conn->query($cambio)) === true) {

I see too many open and close keys () , in fact I did a test, and I send an error.

  

error: Fatal error: Call to a member function query() on null in... , like on that line.

You could do something like this:

$result = $conn->query("UPDATE Usuarios SET name='$nombre', email='$emai', password='$pass', phone='$tel', address='$dir' WHERE ID=$id"); 

if (true===$result) { }

or

if ($conn->query($cambio) === true)      

A possible example:

conexion.php

$conn = new mysqli("servidor", "usuario", "contraseña", "BaseDatos");

/* verificar conexión */
if (mysqli_connect_errno()) {
    printf("Conexión fallo: %s\n", mysqli_connect_error());
    exit();
} else {
    //echo 'Existe conexión.';
}

UPDATE

<?php
    session_start();        
    //Reset
    $nombre = $emai = $pass = $tel = $dir = $id = NULL;

    //Si esta definido el formulario
    if (isset($_POST['sumbitt'])) {     
        //Obtener datos del formulario
        $nombre = $_POST['nombre'];
        $emai   = $_POST['emai'];
        $pass   = $_POST['pass'];
        $tel    = $_POST['tel'];
        $dir    = $_POST['dir'];
        $id     = $_SESSION['usuario']['ID'];

        //Si esta definido la sesion.
        if (isset($_SESSION['usuario'])) {
            //Verdadero datos a trabajar.
            if ($nombre && $emai && $pass && $tel && $dir && $id) {
                //Conexion (Importante llamar a la conexión dodne vas a trabajar con el).
                require 'conexion.php';
                //Sentencia
                $result = $conn->query("UPDATE Usuarios SET name='$nombre', email='$emai', password='$pass', phone='$tel', address='$dir' WHERE ID=$id");        
                //Comprabación si se ejecuto la sentencia.
                if (true===$result) {
                    echo $_SESSION['usuario']['name'];
                } else {
                    exit('Fallo el update: ' . htmlspecialchars($conn->error));
                }                   
            }
        } else {
            echo"oops hubo un error en tu sesión.";
        }   
    }

?>

  

Note: I advise you for security use mysqli prepare statements or PDO. I also advise you to read well    How to avoid SQL injection in PHP ?