I've built several Google Actions and Alexa Skills recently, and while Alexa seems to be pretty straightforward in terms of finding and adding Skills to your devices via the Alexa app / Skill store, the Google Home situation with Google Assistant isn't as straightforward.
To be honest, there still appears to be some "friction" in this experience that is eventually supposed to be "frictionless."
I will tell you, like most Google "situations," the answer is actually pretty simple, it's just not easy to find it.
So nevertheless, once you know which app to use to add your Action via, there will be no problems.
That's just it my friends, don't look in the Google Home app to find your actions, look in the Google Assistant app!
It's that easy. This video shows you what I mean.