Reading your requirements, Azure App Configuration is the service offering you can leverage. Each app and read this configuration for any settings/values required for your app. An added benefit is the concept of labels, also known as feature flagging. If one of your app services requires a different setting, you can append a label to the app setting which allows you to maintain the same setting name but load a different value based on the label. Another benefit is the SDK offering for App Configuration can reload app settings when the configuration store is changed.
If your global config is a bit more complex i.e., objects, you can still leverage app configuration settings and use it conjunction with Cosmos Db, where the app config directs your app to particular Cosmos instance and/or item. For changes, you can leverage Cosmos' change feed feature where your app gets a "notified" of a change.