Google OAuth – Mail In Sent Folder But Not Appearing Back in Inbox

So using Post SMTP and everything is authed and seems to be working fine. The issue comes is with booking confirmations coming back into the business. These appear in the sent items on gmail so are sending but are not then appearing in the Inbox? I assume this is something to do with them being authed off-site perhaps?

I have tried same email addy and also alias ones but the booking confirm / edit / cancellation only goes to the customer and not back to the business. Thanks

Mailer: postsmtp
HostName: xxxx
cURL Version: 7.58.0
OpenSSL Version: OpenSSL/1.1.1
OS: Linux xxxxx4.15.0-204-generic #215-Ubuntu SMP Fri Jan 20 18:24:59 UTC 2023 x86_64
PHP: Linux 7.4.33 C.UTF-8
PHP Dependencies: iconv=Yes, spl_autoload=Yes, openssl=Yes, sockets=Yes, allow_url_fopen=Yes, mcrypt=Yes, zlib_encode=Yes
WordPress: 6.0.3 en_GB UTF-8
WordPress Theme: shave
WordPress Plugins: Shave Custom Post Types & Taxonomies, Advanced Custom Fields PRO, Advanced Custom Fields, Bookly Customer Cabinet (Add-on), Bookly Pro (Add-on), Bookly Staff Cabinet (Add-on), Bookly, Code Snippets, Contact Form 7, Smash Balloon Instagram Feed, NextGEN Plus, NextGEN Gallery, Post SMTP, Slider Revolution, WP Crontrol, SmartCrawl Pro, WPMU DEV Dashboard
WordPress wp_mail Owner: /var/web/site/public_html/wp-content/plugins/post-smtp/Postman/PostmanWpMailBinder.php
WordPress wp_mail Filter(s): wp_staticize_emoji_for_email, WordPress_StatsD->wp_mail, PostsmtpMailer->get_mail_args
WordPress phpmailer_init Action(s): wpcf7_phpmailer_init
Postman: 2.1.1.1
Postman Sender Domain (Envelope|Message): esquirenorwich.co.uk | esquirenorwich.co.uk
Postman Prevent Message Sender Override (Email|Name): Yes | Yes
Postman Active Transport: Gmail API (https:oauth2://www.googleapis.com:443)
Postman Active Transport Status (Ready|Connected): Yes | Yes
Postman Deliveries (Success|Fail): 61193 | 2259
Postman TCP Timeout (Connection|Read): 20 | 60