Is there a Bentley CONNECTION Client GPO and/or what are the Registry/File settings to control the "Preferences" in an Enterprise Windows Environment?

I am not aware of a GPO for CONNECTION Client, but most of the desired behaviors can be implemented through other methods. All of the settings are managed by a SQLite database in each user profile at %LocalAppData%\Bentley\MySELECT.db. They are stored in the Settings table and can be modified there. To do this in a programmatic fashion, I suggest modifying the database using PowerShell and a third-party SQLite PowerShell module named PSSQLite.

Skip the “Get Started” intro on first start

Modify the OnboardingShown key in the Settings table. To do this through PSSQLite, use the following command:
Invoke-SqliteQuery -Query "update Settings set Value='True' where Key='OnboardingShown'" -DataSource "$env:LocalAppData\Bentley\MySELECT.db"

The command above has been edited since this response was originally posted to correct a logic error.

Run the CONNECTION Client on system startup

As you already discovered, the auto-start of CONNECTION Client on system startup can be disabled by executing the following command, but there is one caveat below:
reg delete HKCU\Software\Microsoft\Windows\CurrentVersion\Run /v MySELECT.exe /f

Important: Auto-startup is strongly recommended if you are running V8i and earlier versions of Bentley products since these versions do not necessarily start the CONNECTION Client when opened. This ensures that all usage is properly associated with a Bentley user account.

Automatically sign me in

Modify the AutoLogin key in the Settings table. To do this through PSSQLite, use the following command:
Invoke-SqliteQuery -Query "update Settings set Value='False' where Key='AutoLogin'" -DataSource "$env:LocalAppData\Bentley\MySELECT.db"

Minimize CONNECTION Client after sign in

Modify the MinimizeOnSignIn key in the Settings table. To do this through PSSQLite, use the following command:
Invoke-SqliteQuery -Query "update Settings set Value='True' where Key='MinimizeOnSignIn'" -DataSource "$env:LocalAppData\Bentley\MySELECT.db"

Show Desktop Notications and set the Check and Retrieve messages days.

Modify the ShowDesktopNotifications, Notifications.RefreshIntervalInSeconds, and Notifications.RetrievalGoBackDays keys in the Settings table. To do this through PSSQLite, use the following commands, modifying them as needed:
Invoke-SqliteQuery -Query "update Settings set Value='True' where Key='ShowDesktopNotifications'" -DataSource "$env:LocalAppData\Bentley\MySELECT.db"
Invoke-SqliteQuery -Query "update Settings set Value='60' where Key='Notifications.RefreshIntervalInSeconds'" -DataSource "$env:LocalAppData\Bentley\MySELECT.db"
Invoke-SqliteQuery -Query "update Settings set Value='30' where Key='Notifications.RetrievalGoBackDays'" -DataSource "$env:LocalAppData\Bentley\MySELECT.db"

In addition, is there a way to have the CONNECTION Client exit automatically when the last Bentley product is closed since it automatically opens when the first Bentley product opens?

No, only CONNECT Edition versions of products will launch the CONNECTION Client if not already running. To ensure that usage for V8i and earlier versions are associated with a Bentley user account, the CONNECTION Client is designed to remain running in the background. If only CONNECT Edition versions of products are installed, users can exit the CONNECTION Client after Bentley products have been closed, but again, it has been intentionally designed to stay out of a user's way.

Thanks Jeremy for the quick response.

Daniel did you come up with a complete install for the Enterprise with all your settings?

Daniel did you come up with a complete install for the Enterprise with all your settings?