Open the Drive app, tap the "New" button, and select "Upload". You get a file picker UI. This UI is provided by the Storage Access Framework that Nextcloud says they cannot use.
This is not the same functionality that Nextcloud provides though. This is one time upload of manually selected files, not ongoing passive sync of an entire directory tree.
That's just the Drive app. The system overall certainly has more capabilities than are made available to developers[0].
[0]: https://support.google.com/googleone/answer/9149304?hl=en&co...