Your estimate
A native app is the format that fits
Format: native app
Your answers contain a technical requirement that only an installed app can carry: the solution has to get so close to the phone operating system and hardware that only an app downloaded from the App Store and Google Play handles it reliably on both iPhone and Android. The format is settled by the technology, then. Whether the project is ready to be developed is a separate question: the project maturity below answers that, and it does not change the format.
Assumptions behind the estimate
That the technical requirement is real and cannot be sidestepped with a simpler workflow. It is worth testing before it is allowed to cost anything.
What would change the answer
If the requirement turns out to be manageable in the browser, or the workflow can be simplified, a web app or a self-service module becomes the cheaper route.
What a discovery call would answer
The smallest useful version of the app, the technology choice that follows from the need (Flutter or native, for example), and what running it and the app stores realistically demand.