CiviMobileAPI Extension vs APIv3 for mobile app integration
The CiviMobile API extension was developed specifically for the CiviMobile App. It's not a generic end point for other apps to use. If you were planning on using it in this way, then at the very least it would be wise to reach out to those developers to let them know that this is what you were doing, so they might re-consider implementing breaking changes.
CiviMobile is a closed source app. Open source back-end extension.
For comparison, CiviContact is open source app and open source back-end extension, https://civicrm.org/blog/justinfreeman/civicontact-for-android-and-ios-released-manage-civicrm-contacts-groups - and was developed as a platform, reference for building other CiviCRM mobile apps. Although, no one so far has taken up that challenge.
Both apps utilise a back-end extension to provide API end points for the app. That's a valid model to follow.
The question really should be whether or not CiviCRM APIv3 or CiviCRM APIv4 should be used. Given that at this point in time v4 does not have a REST end point implementation, any integration which uses REST must therefore use APIv3.
There's no problem in mixing and matching APIv3 and APIv4 calls. Since they both work fine and APIv3 is not going to be deprecated anytime soon.
Personally, I would use Flutter for any new app development. That's just my opinion - do you own research.