Oh, it does save the password.
Oauth makes sense that there's no password saved. A unique key is saved which is authenticated with Google. If this key leaks, you are hosed, too, but at least you can revoke that key.
I tried grep mypasswd ~/.nylas-mail/* and grep said Binary file shared.sqlite matches. This did not occur in ~/.nylas it makes sense and it is inevitable, a client like Thunderbird suffers from the same.
It can be circumvented by saving the password encrypted and decrypting it using a master password. That is akin to how LastPass and Mozilla save their cloud data.
Using containers etc would also lower the threat.
In a way its good the password is saved locally. The engine also runs locally. It moves the threat model to the client, away from Nylas servers. Kudos.