The new 'Settings' mechanism of VB.NET 2.0 and the related My.Settings object make it convenient to add new settings and to access the configuration settings from code as strongly typed data.
To bad that the project 'Settings' property page does not show e.g. <connectionStrings> settings imported (copy-paste) into the "Syden.Trio.ClientApp.exe.config" file from the config files of other assemblies, such as the typical "Syden.Trio.DataAccessLogic.dll.config" file which most likely contains the database connection string. Neither will these non-native configuration settings be available in the My.Settings object.
If you want to have a single config file, i.e. not use multiple .dll.config files in addition to the .exe.config file, you must use the ConfigurationManager class to access non-native (imported) settings. This class gives provides a .ConnectionStrings collection, in addition to the classic .AppSettings collection.
Thus, to get to the connection string used by generated TableAdapter code, use code like this:
configInfo.Text = ConfigurationManager.ConnectionStrings
Note how VB.NET use the assembly's full namespace to prefix all config settings. This is why My.Settings does not like/support imported settings.
The ConfigurationManager is new in .NET 2.0 and requires you to add a reference to the System.Configuration assembly.