Custom domains with GMail used to be free for the longest time, until Google started changing their pricing policy. The final free option disappeared in 2014. [1] This article points out a hacky way of still getting it free.
[1] All previously acquired free accounts are grandfathered, this is all about making new accounts.
I wasn't grandfathered in. I did a similar process to what the OP did. My point was just that you need not use mailgun. All you need are the settings from your smtp to plug into gmail and that's nothing new.
I've also have been doing this for over a year now. When I compose a email, there is a drop down for what domain I want to send from.