Unfortunately it is up to the individual apps, such as Nextcloud, whether or not they allow other apps to choose a folder from the document picker UI. A number of apps such as Dropbox, etc do the same and folders appear greyed out in other apps, and they only allow you to pick individual files. I did hope when I implemented the "Choose a folder" method that not so many apps would disable choosing a folder and it would enable a wide range of sync methods to be used with beorg. You'll find some apps do allow this, such as Working Copy so that you can sync with a git repository, however they are in the minority.
Oh, I wasn't aware of the difference between selecting files and selecting a folder. That's too bad. Thanks for the info!
For any future searchers: Ironically, a Nextcloud iOS client user just opened an issue for this, if you'd like to follow it. I've commented there.
I tried switching to the Nextcloud Files location using the "Choose a folder" method, but it was disabled.
With the Files app being a unified place for cloud storage providers to expose files on iOS nowadays, it might make your life somewhat simpler to enable users to choose remote locations and centralize new development on that backend rather than having to maintain your own WebDAV, Dropbox, and Box backends, etc.
Most modern iOS apps use the Files backend to defer all networking and account configuration to iOS and cloud provider apps, allowing the third-party app to focus on its features. This also limits requests for permissions like network access, which means users don't have to trust the developer as much.
Since Beorg has a long history, maybe freezing new features for the other backends is a good middle ground for now? Then you could still allow current users to continue using Beorg in its current state if they don't want to switch to the Files backend for some reason.
I would happily pay for this "feature", if that's what's holding you back. Otherwise, you could just enable it now, and make new paid features (like Roam support) only support the local Files backend.