How can I make the Uploaded field editable for Media Library?

It doesn’t look like you called global $wpdb at the top of your function to access the $wpdb class. However, I’m not sure you’re actually even getting to that part in your edit_attachment callback.

You are trying to access the 'media_date' property of the request, but looks like you are actually setting the name of the input to 'post date'. You’re also using $post_id and not $attachment_id in your function.

Here’s your code cleaned up, hopefully this works for you.

function jch_attachment_fields_to_edit( $form_fields, $post ){

    $post_date =  $post->post_date;

    $form_fields['post_date'] = array(
        'value' => $post_date ? $post_date : '',
        'label' => __( 'Uploaded Date' )
    ); 


    return $form_fields;
}
add_filter( 'attachment_fields_to_edit', 'jch_attachment_fields_to_edit', 10, 2 );

/**
 * Update attachment metadata 
 *
 * @param int $post_ID Attachment ID.
 */


function jch_edit_attachment( $attachment_id ){

    if ( empty( $_REQUEST['attachments'][$attachment_id]['post_date'] ) ) {
        return;
    }

    $date = $_REQUEST['attachments'][$attachment_id]['post_date'];

    // Make sure the date is in the correct format here... Sanitize as well...

    wp_update_post([
        'ID'            => $attachment_id,
        'post_date'     => $date,
        'post_date_gmt' => get_gmt_from_date( $date )
    ]);

}
add_action( 'edit_attachment', 'jch_edit_attachment' );

You’re going to want to make sure whatever date is going into the DB is going to be in the correct format, so you’ll want some validation as well.