My current workaround for the lack of direct integration is as follows:
From the Bryton Active App (on iphone ) Click on the … in the top right hand corner
The select export FIT File
I then have an option to choose a location and as I have a dropbox account and app that option shows up in the screen below
The iPhone remembers the last used location therefore on interval.icu under Setting / Connections I have setup a Dropbox location to pull files from
Not 100% automatic but quite quick to do from the Bryton App.
I believe you can still create a free Dropbox account that has 2GB of space associated with it.