Re: is there a way to set a primary gmail account / other google accounts?
In the past, that is, years ago, you could only sign in with one Google Account at a time. This means that you always had to sign out of the account before signing in with another account. Then people wanted to not log out. Now the opposite is true.
So. In response to your question, you must sign out manually. Otherwise, you will naturally be logged out if you close the device or devices associated with this account, but your data will be stored on your devices. For example, in cookies, web browser memory (most recently used, session, etc.) and as soon as you open this device, you will be automatically signed in to the account you last used.
If you do not wish to do so, you must always log out and, if necessary, clear cookies and/or usage history before shutting down your device.
You can do it automatically, if want. Most of devices have such a settings. If not, You can use special script to log out and delete cookies, etc. The script is simple to write, but it is different for every user, so You must make Your selection, but the simplest way is to logging off.