In order to post a Tweet, you need a user context (i.e. logged in user), and that is why TWTRComposer wants to be connected to a Twitter account. Pre-iOS 11, this was achieved with the OS-level accounts where the user granted access in iOS. Post-iOS 11, this has to be done on an app-by-app basis. We recognise that the OAuth scopes are not very granular, but at the moment there are no plans to change this.
You’re free to use the iOS share sheet instead, or the custom URI you mentioned, but that doesn’t include adding an image.