You are only logged into AGOL when Pro is running or a script is running that uses Pro's ArcPy. When you close out of Pro or the script terminates, you will be logged out.
If there is a security issue, or potential issue, it might be allowing Pro to automatically log you in because it means Pro is storing one's credentials. That said, Pro encrypts the credentials it stores and there are bigger problems if your Windows or Active Directory profile has been compromised and someone else is using your profile or machine.
The only time I actively log out of AGOL from within Pro is when I am switching from AGOL to an internal portal for licensing.
