How to add custom fields to WooCommerce product data panel - wordpress

Question

I have created a custom product type for events in WooCommerce. Now I want to add some custom fields to it.
This can be achieved with functions like woocommerce_wp_select(), woocommerce_wp_text_input() etc. However, as far as I know, whith these function you can only add text input fields, textarea's, select boxes and select dropdowns.
I want to add a date picker field, a file upload field and an url input field.
I have created these fields and they do render on the admin panel as they should, but the values are not saved (although I'm using the action hook 'woocommerce_process_product_meta'). Only the first 2 fields (event_type and event_location), which are created with the WooCommerce function, are stored properly.
What am I doing wrong here?
My code:
add_action('woocommerce_product_data_panels', 'okappi_add_custom_fields');
function okappi_add_custom_fields()
{ ?>
<div id="event_details" class="panel woocommerce_options_panel hidden">
<div class="options_group" class="show_if_event">
<? woocommerce_wp_select([
'id' => 'event_type',
'label' => __('Event type', 'custom'),
'wrapper_class' => 'show_if_event',
'value' => get_post_meta(get_the_ID(), 'event_type', true),
'options' => array('online' => 'Online', 'international' => 'International', 'internal' => 'Internal'),
]); ?>
<? woocommerce_wp_text_input([
'id' => 'event_location',
'label' => __('Event location', 'custom'),
'wrapper_class' => 'show_if_event',
'value' => get_post_meta(get_the_ID(), 'event_location', true),
]); ?>
<p class="show_if_event form-field event_start_date_field">
<label for="event_start_date">Start date</label>
<input type="date" id="event_start_date" name="event_start_date" class="date short">
</p>
<p class="show_if_event form-field event_end_date_field">
<label for="event_end_date">End date</label>
<input type="date" id="event_end_date" name="event_end_date" class="date short">
</p>
<p class="show_if_event form-field event_pdf_field">
<label for="event_pdf">PDF upload</label>
<input type="file" id="event_pdf" name="event_pdf" class="date short">
</p>
<p class="show_if_event form-field event_link_field">
<label for="event_link">Event link</label>
<input type="url" id="event_link" name="event_link" class="date short" placeholder="https://www.my-event.com/">
</p>
</div>
</div>'
<? }
add_action('woocommerce_process_product_meta', 'save_custom_fields');
function save_custom_fields($post_id)
{
$product = wc_get_product($post_id);
$event_type = isset($_POST['event_type']) ? $_POST['event_type'] : '';
$product->update_meta_data('event_type', sanitize_text_field($event_type));
$event_location = isset($_POST['event_location']) ? $_POST['event_location'] : '';
$product->update_meta_data('event_location', sanitize_text_field($event_location));
$event_start_date = isset($_POST['event_start_date']) ? $_POST['event_start_date'] : '';
$product->update_meta_data('event_start_date', sanitize_text_field($event_start_date));
$event_end_date = isset($_POST['event_end_date']) ? $_POST['event_end_date'] : '';
$product->update_meta_data('event_end_date', sanitize_text_field($event_end_date));
$event_pdf = isset($_POST['event_pdf']) ? $_POST['event_pdf'] : '';
$product->update_meta_data('event_pdf', sanitize_text_field($event_pdf));
$event_link = isset($_POST['event_link']) ? $_POST['event_link'] : '';
$product->update_meta_data('event_link', sanitize_text_field($event_link));
$product->save();
}