Solution 1
Well, you can indeed use a textarea, split the posted value into an array, trim the lines, validate that each line contains a valid E-Mail address and do whatever you would like with the mails:
<form method="POST">
    <p>
        <label for="emails">
            One E-Mail per line:
        </label>
        <textarea name="emails" id="emails" cols="80" rows="10">jdsjdhs@sdhjsdhj.de
jsddhs@ssdddhjsdhj.email
jsddhs@sdsddhj.tk
jdsjdsdhs@sdhjsdhj.org
jdsjdsdhs@sdhjsdhj.jetzt</textarea>
    </p>
    <p>
        <input type="submit" value="Validate">
    </p>
</form>
<?php
if ($_SERVER['REQUEST_METHOD'] === 'POST') {
    $emails = explode("\n", $_POST['emails']);
    $emails = array_map('trim', $emails);
    $emails = array_filter($emails, function ($email) {
        return filter_var($email, FILTER_VALIDATE_EMAIL);
    });
    $validEmailCount = count($emails);
    echo <<<HTML
    <p>
        $validEmailCount valid E-Mails found.
    </p>
    HTML;
    // Your database logic here
}
Solution 2
Based on the below comment thread, the OP is looking for an HTML only email "validation".
For that purpose, the input[type=email] is probably the best choice.
To allow as many emails as wanted, I have written the below PHP, which adds a blank email field every time the form is submitted with the checkbox asking for another field is marked as on.
<?php
$emails = [''];
if (
    $_SERVER['REQUEST_METHOD'] === 'POST' &&
    isset($_POST['emails']) &&
    is_array($_POST['emails'])
) {
    $emails = $_POST['emails'];
    if (
        isset($_POST['add_mail']) &&
        $_POST['add_mail'] === 'on'
    ) {
        $emails[] = '';
    } else {
        print_r($emails);
        die;
    }
}
?>
<form method="POST">
    <?php foreach ($emails as $email) : ?>
        <p>
            <input type="email" name="emails[]" value="<?= $email ?>">
        </p>
    <?php endforeach; ?>
    <p>
        <label for="add_mail">
            Would like to enter one more E-Mail?
        </label>
        <input type="checkbox" name="add_mail" id="add_mail">
    </p>
    <p>
        <input type="submit" value="Send">
    </p>
</form>
Solution 3
Another solution would be to use a single input[type=text] in combination with the [pattern] attribute, and write a regular expression for it, that allows multiple email addresses.
<input type="text" pattern="…" required>
The emails could be separated by space, commas or semicolons, for example.
You would then do something like ,? to allow a delimiter or not.