There is no "add user to channel" button in mobile app

I don’t see a way to add a user to a channel in the MM app (android, v2.1). A work-around is to tag the user @user in the channel and then you will be prompted to add the user to channel. However, tagging users in private channels prompts to add them to the channel, but users are not added to private channel.

This is a known “issue”, the “add members” feature has not made it into 2.1, the PR is ready, though, so it should be merged into one of the next releases:

The workaround is, as you already said, mentioning users and then click on the “add user to this channel” ephemeral message that appears after you did that.