There could be several reasons why the connected machine agent isn't showing as being installed.
- The machine does not meet the software requirements of having .NET Framework 4.6 or later and PowerShell 5.1. I would consider this highly unlikely though.
- The account used to install/configure the agent did not have the required permissions, such as being an Ower or User Access Administrator role in the subscription or having elevated privileges on the machine itself.
- Network connectivity issues that prevent the agent from communicating with Azure Arc.
This is just a start, but it's important to check the logs and error messages and refer to Troubleshoot Azure Connected Machine agent connection issues - Azure Arc | Microsoft Learn to better determine what the exact cause could be.