I have my app offline and can't connect it to the internet. How can I make use of Sentry monitoring in this case?

It depends on what kind of setup you have. However, it requires the app to connect to the internet eventually to send information to Sentry.

If you are developing mobile applications, offline caching is supported by all our mobile SDKs, but the app from that specific device would need to connect to the internet eventually in order to send cached events to Sentry.

Similarly, all of our Browser SDKs allow custom transports, which can support offline caching, so that the events can be sent when a connection is restored. We have docs on browser offline caching here.

Fully offline applications are not supported.