Gmail API with WP SMTP Plugins Not Sending to Gsuite “groups”

Question

When we use any SMTP plugins for WordPress with the Gmail API we are unable to receive any WP generated emails to our group email addresses [e-mail] or [e-mail] such as product inquiries, order emails, or contact form emails.

Without the SMTP set up all emails to the groups deliver fine and have for the past 3+ years. When the smtp plugin is active and set up according to these help docs we receive no WP generated emails.

We have tried https://wordpress.org/plugins/gmail-smtp/ as well as https://wordpress.org/plugins/wp-mail-smtp/

These are the associated help docs, respectively: https://wphowto.net/gmail-smtp-plugin-for-wordpress-1341, https://wpforms.com/how-to-securely-send-wordpress-emails-using-gmail-smtp/

The desired result is simply to be able to have WP send associated emails to our group emails and have them be delivered. I checked the gsuite log and they aren't even showing so it looks like the Gmail API is intercepting them and never pushing them to our Gsuite group emails.

Here is the code I saw when debugging:

2019-04-03 21:18:25 Connection: opening to smtp.gmail.com:587, timeout=300, options=array () 
2019-04-03 21:18:25 Connection: opened 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "220 smtp.gmail.com ESMTP c18sm9527617qkk.1 - gsmtp" 
2019-04-03 21:18:25 SERVER -> CLIENT: 220 smtp.gmail.com ESMTP c18sm9527617qkk.1 - gsmtp 
2019-04-03 21:18:25 CLIENT -> SERVER: EHLO dev.equusport.com 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-smtp.gmail.com at your service, [67.205.36.40]" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-SIZE 35882577" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-8BITMIME" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-STARTTLS" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-STARTTLS" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-ENHANCEDSTATUSCODES" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-STARTTLS250-ENHANCEDSTATUSCODES" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-PIPELINING" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-STARTTLS250-ENHANCEDSTATUSCODES250-PIPELINING" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-CHUNKING" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-STARTTLS250-ENHANCEDSTATUSCODES250-PIPELINING250-CHUNKING" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250 SMTPUTF8" 
2019-04-03 21:18:25 SERVER -> CLIENT: 250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-STARTTLS250-ENHANCEDSTATUSCODES250-PIPELINING250-CHUNKING250 SMTPUTF8 
2019-04-03 21:18:25 CLIENT -> SERVER: STARTTLS 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "220 2.0.0 Ready to start TLS" 
2019-04-03 21:18:25 SERVER -> CLIENT: 220 2.0.0 Ready to start TLS 
2019-04-03 21:18:25 CLIENT -> SERVER: EHLO dev.equusport.com 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-smtp.gmail.com at your service, [67.205.36.40]" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-SIZE 35882577" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-8BITMIME" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-AUTH LOGIN PLAIN XOAUTH2 PLAIN-CLIENTTOKEN OAUTHBEARER XOAUTH" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-AUTH LOGIN PLAIN XOAUTH2 PLAIN-CLIENTTOKEN OAUTHBEARER XOAUTH" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-ENHANCEDSTATUSCODES" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-AUTH LOGIN PLAIN XOAUTH2 PLAIN-CLIENTTOKEN OAUTHBEARER XOAUTH250-ENHANCEDSTATUSCODES" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-PIPELINING" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-AUTH LOGIN PLAIN XOAUTH2 PLAIN-CLIENTTOKEN OAUTHBEARER XOAUTH250-ENHANCEDSTATUSCODES250-PIPELINING" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250-CHUNKING" 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-AUTH LOGIN PLAIN XOAUTH2 PLAIN-CLIENTTOKEN OAUTHBEARER XOAUTH250-ENHANCEDSTATUSCODES250-PIPELINING250-CHUNKING" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "250 SMTPUTF8" 
2019-04-03 21:18:25 SERVER -> CLIENT: 250-smtp.gmail.com at your service, [67.205.36.40]250-SIZE 35882577250-8BITMIME250-AUTH LOGIN PLAIN XOAUTH2 PLAIN-CLIENTTOKEN OAUTHBEARER XOAUTH250-ENHANCEDSTATUSCODES250-PIPELINING250-CHUNKING250 SMTPUTF8 
2019-04-03 21:18:25 Auth method requested: XOAUTH2 
2019-04-03 21:18:25 Auth methods available on the server: LOGIN,PLAIN,XOAUTH2,PLAIN-CLIENTTOKEN,OAUTHBEARER,XOAUTH 
2019-04-03 21:18:25 CLIENT -> SERVER: QUIT 
2019-04-03 21:18:25 SMTP -> get_lines(): $data is "" 
2019-04-03 21:18:25 SMTP -> get_lines(): $str is "221 2.0.0 closing connection c18sm9527617qkk.1 - gsmtp" 
2019-04-03 21:18:25 SERVER -> CLIENT: 221 2.0.0 closing connection c18sm9527617qkk.1 - gsmtp 
2019-04-03 21:18:25 Connection: closed