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Today I tried to register an Ubuntu in the latest version (22.04) in Azure to the ARC service. I proceeded as in a previous blog post described.
Unfortunately without success....

# Script-Download
wget https://aka.ms/azcmagent -O ~/install_linux_azcmagent.sh
# Script Execution
bash ~/install_linux_azcmagent.sh

The official installation script doesn't seem to be designed for this yet.

However, it should already be supported, as stated in this link.

I got it to run anyway.

# Rereading the package lists
sudo -E apt update

# Curl Modul - Installation
sudo -E apt install -y curl

# Dept - File Download using Curl
curl https://packages.microsoft.com/ubuntu/20.04/prod/pool/main/a/azcmagent/azcmagent_1.20.02012.246_amd64.deb -o /tmp/azcmagent.deb

# Package installation
sudo -E apt install -y /tmp/azcmagent.deb

# AZCMAGENT - Availability Check
azcmagent

# Connecting Agent
azcmagent connect --resource-group "resourceGroupName" --tenant-id "tenantID" --location "regionName" --subscription-id "subscriptionID" --cloud "cloudName"
# see link: https://it-infrastructure.solutions/onboarding-azure-arc-linux-ubuntu/

References:

https://it-infrastructure.solutions/onboarding-azure-arc-linux-ubuntu/

Generally available: Azure Monitor Agent available on latest Linux distros | Azure updates | Microsoft Azure
Ubuntu 22.04, AlmaLinux, and Rocky Linux now supported via the Azure Monitor Agent.