There are no custom metrics nor custom dimensions in App + Web per se, however, there are equivalent called parameters and user properties.
Where it used to be a hit-scoped custom dimension, you will utilise parameters in the App+Web property and for user-scope dimensions, you will utilize user properties. It must be noted that user properties will require a code to be injected into the web/app.
For App + Web, you can send up to 25 custom parameters per hit sent and similar to current Google Analytics set up, custom parameters are not retroactive which means that it will only collect data once the parameter is enabled.