You could have changed the user and group in one command using openhab:openhab but otherwise the costs look correct.
Set up openhab with the ssh keys for the pi user in the other machine and light into that other machine as pi.
ssh pi@192.168.0.82
You may have to give the pi user permission to run shutdown without a password, but don’t give it nopassword for all commands, just the shutdown command.
Otherwise you will need to create an openhab user on the remote machine and give this user the sudoer permissions.
Finally, the first time you run sudo as a user on a machine you will get the “We trust you have…” message that you must acknowledge. Once acknowledged the message never appears again, so once you give the user on the alarm RPi sudo permissions, you should manually log into the machine and run a sudo command so you can acknowledge that warning message.