Enqueue jQuery script in admin to send email via ajax in a custom WordPress plugin

I’m trying to get a form to work on an admin page on WordPress. I want to be able to input an email address and have it send an email to the email inputted. I’m using a jQuery Ajax function to send the info from the form to the PHP that I am using to send the email. Everything is in a custom WordPress plugin. The code worked when I was testing it in a normal page on WordPress, but since I moved it to an admin page in the plug in, I can’t seem to get it to work.

The JavaScript file at_home-welcome-rev2.js

jQuery(document).ready(function ($) {
    $('#at_home_form').on('submit', function (event) {
        event.preventDefault(); // Prevent the default form submission
        
        var emailInput = $('#userEmailInput').val(); // Get the user's email input
        var nonce = ajax_object.nonce
        console.log(nonce);
        $.ajax({
            url: ajax_object.ajax_url,
            type: 'POST',
            data: {
                action: 'send_email', // Use the updated action name
                user_email: emailInput, // Pass the user's email input
                nonce: nonce
            },
            
            success: function (response) {
                alert('Email sent successfully!');
            },
            error: function (error) {
                alert('Error sending email: ' + error.responseText);
            }
            
        });
        console.log('Data array:', {
            action: 'send_email',
            user_email: emailInput
        });
    });
});

The PHP code:

function enqueue_plugin_scripts() {
    // Enqueue your JavaScript file
    wp_enqueue_script('at_home_welcome', plugin_dir_url(__FILE__) . 'js/at-home-welcome-rev2.js', array('jquery'), '1.0', true);

    // Localize the script with data
    wp_localize_script('at_home_welcome', 'ajax_admin_object', array(
        'ajax_url' => admin_url('admin-ajax.php'), // Default AJAX URL
        'nonce' => wp_create_nonce('at_home_welcome-nonce') // Create a nonce for security
    ));
}
add_action('wp_enqueue_scripts', 'enqueue_plugin_scripts');
function at_home_menu_page() {
    add_menu_page(
        'At Home Care Certification Form', // Page title
        'AT Home Care', // Menu title
        'manage_options', // Capability required to access
        'at-home-care', // Menu slug
        'at_home_care_settings_page_callback' // Callback function to display content
    );
}
add_action('admin_menu', 'at_home_menu_page');

function at_home_care_settings_page_callback() {
    ?>
    <div class="wrap">
        <h1>Your Plugin Settings</h1>
        <form id="at_home_form">
            <label for="userEmailInput">Enter your email:</label>
            <input type="email" id="userEmailInput" name="userEmailInput" placeholder="[email protected]">
            <button type="submit" id="sendEmailButton">Send Email</button>
        </form>
    </div>
    <?php
}

// AJAX action to send email
function at_home_welcome_send_email_callback() {
    if (isset($_POST['user_email'])) {
        $to = sanitize_email($_POST['user_email']); // Sanitize the user's email input
        $subject = 'Your Membership has been approved';
        $message = 'Welcome, we hope you enjoy your membership';
        $nonce = $_POST['nonce'];
        error_log('Received email: ' . $nonce);
        // Verify nonce
        if (wp_verify_nonce($nonce, 'at-home-nonce')) {
            error_log('Received email: ' . $to); // Check the email value in PHP error log
            // Send the email
            $sent = wp_mail($to, $subject, $message);
        } else {
            wp_send_json_error();
        }

        // Return the response
        if ($sent) {
            wp_send_json_success();
        } else {
            wp_send_json_error();
        }
    } else {
        wp_send_json_error();
    }
}
add_action('wp_ajax_send_email', 'at_home_welcome_send_email_callback');
add_action('wp_ajax_send_email', 'at_home_welcome_send_email_callback');

I’ve tried about everything I can think of with no success. I would appreciate any feedback or suggestions for things I might try.