Include chat (HTML, js, css) in all pages of WordPress

Try to include your inline script at the bottom of your snipper.js file, and then enqueue it using wp_enqueue_scripts():

function my_chat_script() {
    wp_enqueue_script( 'chat-js', 'URL OF SNIPPER HERE', false );
}
add_action( 'wp_enqueue_scripts', 'my_chat_script' );

This is the proper way to include scripts in your WordPress using functions.php file.

However, if you insist on adding them separately, you can use wp_add_inline_script():

function chat_script() {
   wp_enqueue_script( 'my-chat-script', 'SNIPPER URL HERE', array(), '1.0' );
   wp_add_inline_script( 'my-chat-script', 'SERVICE_PATTERN_CHAT_CONFIG = {appId: '0ef0636b4c36497b866322a096926049', clientId: 'WebChat',apiUrl: 'https://poc.3d2b.ccaas.becloudsolutions.com:9443/clientweb/api/v1',tenantUrl: '3d2b.com',width: 300,chatPath: ''};' );
}
add_action( 'wp_enqueue_scripts', 'chat_script' );

This will output your snippet and inline script separately.