Bluetooth API with a single device

I want to use nuki smart lock for the door of my gym. The mechanism should be very simple: a user authenticates to the tablet that is right before the entrance, and if the authentication goes well, the tablet should do an api call to the smart lock to open the door. How can I do it? I’m reading the api docs but I find it very hard to understand. For ulterior details, the app used in the tablet to let the users authenticate is in flutter.
Thank you

I would use my own system to authenticate and open the lock/door via API after a successful authentication.

So on which part is your problem?

In my opinion, it could be useful to use home
assistant, for example, to have more control. To check, that the door is closed in a time range of x seconds and similar.