Where is the Adroid client manual?

The newest Android client has version 3.7.2, but the latest manual I’ve been able to find is for version 1.0.0. (That manual is available here: https://docs.nextcloud.com/android/ .)

Is there really no newer user’s guide for the Android client?

Yes, unfortunately this is the latest version. I think, however, that the client does not necessarily need its own manual.