Each device has an external storage (/storage/emulated/0/). So uninstall the app, reinstall and you should be be ask for WRITE permission.
The problem here is that the camera issue (Fix camera failure on Android 10 by ewpatton · Pull Request #1957 · mit-cml/appinventor-sources · GitHub) has not yet been resolved in the current version of AI2. However, it has already been fixed on a test server (from @ewpatton), I checked it. Test this app that was created with this server:
https://drive.google.com/file/d/1fhG3KUcbUal54xrJSo-eOwjokN2N5hZG/view?usp=sharing
No need to ask for WRITE permission because the camera component does it automatically.
So you can only wait for the next update ...
Note:
To give users more control over their files and to limit file clutter, apps that target Android 10 (API level 29) and higher are given scoped access into external storage, or scoped storage, by default. Such apps have access only to the app-specific directory on external storage, as well as specific types of media that the app has created.