By accessing your Google account from an unknown device, they know things such as your IP and device details. By sending a push notice to your phone they can have the Google app automatically respond, one example is the Google verification app asking if it's really you logging in, another is Gmail notifying you of new mails. In any case, when nothing responds they know your mobile device doesn't have g apps installed.
It's all done server side, your device isn't leaking more than any other device.
What you could do is set up your own email server (there's easy solutions available, any noob should be able to do it, there's visual "click here, select server name. Want SSL? OK, all done" solutions for less than 2 dollars a month, have Gmail automatically forward all new mails to your personal server and reply to all incoming messages that you've changed email address.
A few months ago I purchased a Samsung Galaxy A7 with the full intention of De-Googling my phone. I installed LineageOS without the Google Apps and I purchased a completely new SIM card that was not associated with my previous google activities. Aside from YouTube, which I accessed with NewPipe, I didn't use a single Google application or service.
Last week, I found out that my bosses boss was still using my old GMail and had sent some fairly important messages to my old account. Rather than waiting several days for my technologically inept boss to resend the emails, I figured "Fuck it, what's the worst that can happen?" and I checked my old GMail using K-9 Mail. I instantly received an Email from Google warning me about an unknown device logging into my account, which I confirmed as safe. Then I immediately received another Email announcing that my phone was not running Google Apps and it offered me a huge ass list of programs that I could be running.
I know that Google owns and develops the Android Open Source Project, but it's still surprising that they could find out my device was Google free after I checked a few emails.