Android version: 10
Device model: SHIFT6mq
Stock or customized system: Stock
Nextcloud app version: 3.13.1
Nextcloud server version: 18.0.3
Reverse proxy:

This will be fixed with 3.14, you can already test it with latest dev version.
Thanks for letting me know. Any ETA for the 3.14 release?
Release Candidate might be available next week, so ETA of the final release is ~3 weeks
I just tested Nextcloud Dev 20200927 and for me the problem is still there.
The buttons have changed. Now one can radio between 'Read only', 'Allow upload and editing' and 'File drop (Upload only). When selecting 'Allow upload and editing' there is still the empty button. The buttons for the other two options work.

Can you give me a screenshot, so that we can compare?
Looks like this is not necessary anymore! It works now as expected with the latest dev version 20201017. However it also works with 3.13.1.
Yesterday the cloud was updated to version 20.0.0. So I guess this is an issue with the server version!