Apache Site Goes To Wrong Page If I Manually Enter HTTPS:// in the URL

Neither of these covers the example.com, and the default site is used, instead:

ServerName www.example.com 
ServerAlias *.example.com

If your certificate is a wildcard certificate for example.com, you could add it to your ServerAlias:

ServerName www.example.com 
ServerAlias example.com *.example.com

It is also possible to avoid using mod_rewrite altogether by adding another VirtualHost *:443 block:

<IfModule mod_ssl.c>
    <VirtualHost *:443>
        ServerName www.example.com
        #...
    </VirtualHost>

    <VirtualHost *:443>
        ServerName example.com
        ServerAlias *.example.com

        Redirect permanent / https://www.example.com/

        SSLCertificateFile /etc/letsencrypt/live/www.example.com/fullchain.pem 
        SSLCertificateKeyFile /etc/letsencrypt/live/www.example.com/privkey.pem
        Include /etc/letsencrypt/options-ssl-apache.conf
    </VirtualHost>
</IfModule>