how to validate the format of an email with php

In this type of case, it is convenient to do a double validation: on the client side and on the server side.

On the client side

Since HTML5 there is the type emailfor the elementsinput , so you put this:

 <input type="email" id="email" class="boton" name="email" placeholder="Tu email">

It will validate the email on the client side.

server side

You can use filter_varto validate the email.

Since it filter_varreturns the validated data or FALSE, you can therefore capture the email directly like this:

$email =  filter_var($_POST["email"], FILTER_VALIDATE_EMAIL);

And then the ifwould be as you have it originally in the code:

if ($email && $name && $message){
    // ... código
} else {
    // ... código
}

To solve the problem you describe there are two ways to do it.

First option:

In this case, the simplest thing you can do is change the attribute of the input where the email is typed in this way type="text"by type="email".

<input type="email" id="email" class="boton" name="email" placeholder="Tu email">

Second option

Use the Jquery Validation plugin with which you validate the form and in addition to that you can show your own error messages.

Here I leave you the code of how your form would look applying the Jquery Validation plugin

1° Have the HTML form

<div id="contact_form">
  <form action="confFormulario3.php" id="form1" name="form1" method="post">
    <input type="text" id="email" class="boton" name="email" placeholder="Tu email">
    <input type="text" id="nombre" class="boton" name="nombre" placeholder="Cómo te llamas">
    <textarea name="mensaje" id="mensaje" class="boton"  placeholder="En qué podemos ayudarte?"></textarea>
    <input type="submit" name="Submit" id="buttonEnviar" class="boton" value="ENVIAR">
  </form>
</div>

2° Create a Javascript file where the corresponding validations are performed, which I will callvalidacion.js

$(function(){
  $('#form1').validate({
    //En rules defines los campos que quieres validar, con el nombre de los id de cada input
      rules: {
        email: {
          required: true,
          email: true
        },
        nombre: {
          required: true,
          minlength: 3
        }
      },
      //En messages describes el mensaje que quieres el usuario visualice por cada cada validación que aplicaste en rules
      messages: {
        email: {
          required: "Este campo es obligatorio",
          email: "El email no tiene el formato correcto"
        },
        nombre: {
          required: "Este campo es obligatorio",
          minlength: "El nombre debe tener al menos 3 caracteres"
        }
      }
}
});

NOTE: For this to work, don't forget to include the plugin library and make the call validacion.jsinside the file where your HTML form is located, otherwise it won't work. I recommend you read the documentation on its official page since the example that I show you is a basic one of the many things you can do.

https://jqueryvalidation.org/documentation/

Perhaps this can help you to do the validations you need and also to insert into your database:

HTML (contact.html)

<form action="javascript:void(0);" method="post" id="form-contacto">
  <input type="text" id="nombre" name="nombre" placeholder="Nombre" onkeypress="return alfabetico(event);">
  <input type="email" id="email" name="email" placeholder="Mail">
  <input type="submit" id="enviar" name="enviar" value="Enviar">
</form>

JS (validations.js)

$(document).ready(function() { 

    $("#enviar").click(function(e){
        e.preventDefault();
        $("#form-contacto").submit();
    });

    $("#form-contacto").validate({
        rules: {
            nombre: {
                required: true
            },
            email: {
                required: true,
                emailExt: true
            }
        },
        messages: {
            nombre: "Ingrese Nombre",
            email: {
                required: "Ingrese Email",
                email: "Ingrese un Email válido"
            }
        },
        submitHandler: function (form) {
            $('#enviar').attr("disabled", true);
            enviarForm();
        }   
    });
});

function enviarForm(){
    var parametros = {
        nombre: $('#nombre').val(),
        email: $('#email').val()
    }

    $.ajax({
        data:  parametros,
        url:  'procesar.php', /* Aqui mandas a tu archivo php para insertar los datos */
        type:  'post',
        async: false,
        success:  function (response) {
            /* Puedes elegir entre mostrar un alert o llevarlo a una paginas estatica des respuesta*/
            alert ("Tus datos se enviaron de forma exitosa!");
        },
        error : showError
    });
}

function showError(XMLHttpRequest, textStatus, errorThrown) {
    alert("Ha ocurrido un error procesando la información");
}

/* Validador alfabetico */
function alfabetico(e){
    kc=e.keyCode?e.keyCode:e.which;
    if(kc<32) return true;
    kc=String.fromCharCode(kc);
    if(/[^a-zA-ZüÜáéíóúÁÉÍÓÚñÑ ]/.test(kc)) return false;
}
/* Validador de Correo */
jQuery.validator.addMethod("emailExt", function(value, element, param) {
    return value.match(/^[a-zA-Z0-9_\.%\+\-]+@[a-zA-Z0-9\.\-]+\.[a-zA-Z]{2,}$/);
},'Ingrese un Email válido');

In your php file, all you have to do is take the data and insert it into your database, the rest (validations) leave it to the JS file. I hope it helps you !