How do I programmatically know which run-mode the instance is running? I created a custom tag that provides the config depending on the instance run-mode, but I can not dete
SlingSetttings is the right way - If it's from Java the simplest way to get it is with an SCR @Reference annotation in a class that's an SCR @Component, saves you from having to go through BundleContext.
If it's from a Sling script, you can use sling.getService(....) to get the SlingSettings.
Note that the cases where you need to read the run modes are rare, usually you'd rather setup your OSGi configurations to depend on the run modes and have the OSGi components modify their behavior based on that.