I’m brand new to all this and so overwhelmed. I don’t understand what can track what or how to block things … but I am going to learn.
I got NordVPN. I set up Protonmail last night (so easy! Loved that). Now how do I keep my new found anonymous existence? I know to use aliase emails on accounts. But to have my new email on my phone, I have to sign into the main account…
Im not sure I want to go to a dumb phone. And I realize my phone IS a tracker … ack. Thanks for your time.
Consider moving to Mullvad or IVPN or ProtonVPN itself. They are superior to Nord.
It is important to not conflate privacy with anonymity. If anonymity is what you want, you should be using TailsOS and everything over Tor. If you want privacy, there are other measures you need to take apart from simply using a VPN. Privacy and anonymity are not the same thing. Always keep that in mind.
To answer your title question: If using ProtonMail app on your Android, Google can know that you downloaded that app and likely use it for your email too. They can’t know of any contents within your Proton account. Unless using GrapheneOS without Play Services and Play Store, Google will likely always know that you use ProtonMail.
Do you consider this outing to Google? I don’t think you should.
And if you’re worried about being tracked, double check your Location settings and harden your device with all settings you can find to tighten up your settings privacy wise.
As @SmartCondor writes, they would know that you use ProtonMail, not your account details or the contents of your mails (unless said mail is sent to a Gmail user, of course).
I also just want to say welcome to the forums. 
Kudos for taking action and working towards improving your privacy. It can definitely be daunting, especially before you’ve established some fundamental knowledge to build on top of.
It’s OK to take things one step at a time, just like improving your lifestyle in general. Privacy Guides has a nice article about it here: Privacy Is Like Broccoli - Privacy Guides
Beyond that, have you looked into threat modelling? It’s a shorthand for getting structured about what you want to protect, from whom, and at what cost. It makes choosing solutions less daunting because you’ve already established your goals and scopes. PG has a nice starting point: Threat Modeling: The First Step on Your Privacy Journey - Privacy Guides
Google will notice all of your account providers sending emails to confirm you wish to change your email address to an atpassmail alias. Sounds good to me!