Everything worked fine until I added in the body text. After that, I no longer received the notification, even though it showed as sent in WP Mail Log.
Then we have made a great step, once again, towards excluding conflicts and limiting the area of infection ( 😛 )
The notification body, as I see on your site, does hold quite some data.
Please follow as below:
1. Ensure, to 100%, that notifications work in your current live install just fine when you remove the content from the body of the notifications
2. Just to be sure, also remove the JS from the Form to test if that has any effects - and if not, then adjust the script to the proper syntax. You should always use "jQuery" instead of "$", see https://toolset.com/documentation/user-guides/adding-custom-javascript-views/#achieving-great-results-with-little-coding-by-using-jquery
3. If at this point you can still positively confirm that the Notification works only if the notification body is omitted, please start with these steps:
- insert the full notification body as you have it now and start subsequently to remove parts.
==> Start with [wpv-user field="user_firstname" id="%%USER_USERID%%"].
==> If not working, remove all HTML
Note, I tested this on the testing site I made, with your HTML and I received the Email but it did not execute the ShortCode [wpv-user field="user_firstname" id="%%USER_USERID%%"].
Forms support HTML and even ShortCodes in the notifications, and should hence not conflict with other Plugins sending them, as the exchange to plain text is done before sending the email, hence, the ShortCodes at this point (inclusive HTML) should be executed.
It was not executed (the shortcode) on the test site because Views was missing - so after installing Views, that part also worked flawlessly
Given the exact same form works on the testing site with the same plugin settings and SPMPT - the only variable left is the server itself and the Google Application you created.
In this case, remains to test with a new Google Application, and if that does not solve the issue, then eventually server admins (and the logs of the servers) may help to narrow down where the sending fails.
Note, you are free to change the SMTP Settings in the testing site and try again - that can show whether your Google API is properly configured or not.
The very last trick I'd resource to is to take the testing site we have now, and add everything you have on the live site to the testing site, to either see when it starts failing or, which I suspect, it should then work just fine.