What do you mean by offline? Don't we need to be online if we need to make an API call?
It's nice to have the option to not need an entire online apparatus to make your software function.
If you're designing your own API, you can do all the specs, docs, and if you get it up and running on localhost, you don't even need internet for testing it.
If you want to run a hosted API endpoint, or push your changes to git ofc you'll need the internet, but not because of the application, rather because you're trying to access something else that is not offline.