The Pro.settingsConfig is not actually used with an Add-In, rather it sets default behavior for ArcGIS Pro on startup. The config file is just a human readable text file. The easiest way to point to this is to add the ADMIN_SETTINGS_PATH command line parameter during an ArcGIS Pro silent installation, The second way to configure client machines is by editing the Windows Registry. Use this option if ArcGIS Pro is already deployed or if you don't want to do a silent installation. To configure the client machines, create a string value called AdminSettingsPath in HKEY_LOCAL_MACHINE\SOFTWARE\ESRI\ArcGISPro\Settings. Set the value data to the path of the network share or local folder that contains the deployed Pro.settingsConfig file.
Some XML Tags you could include in your config file are shown at https://pro.arcgis.com/en/pro-app/latest/get-started/administrator-settings-list.htm
Have you considered revising how your Add-In works to take advantage of a Tabbed Interface?
