You don’t get the message back when you PRIVMSG, you may get a USERSTATE.
Clients are not sent back the messages they themselves send. So normally you will not get a Server response to a PRIVMSG (other than the USERSTATE, if commands CAP is enabled)
This indicates the logged in user, doesn’t have the moderator role in #otherchannels and/or the oAuth key used to login to chat doesn’t have the channel:moderate scope applied to it.
That would suggest other channel is in followers only mode and the authenticating user is not a follower? You should get a error message back as a NOTICE with the tag msg_followersonly. if you have the COMMANDS and TAGS Caps enabled