It's not possible to run the Task Manager GUI on a remote computer, but using the tasklist cmdlet you'll be able to retrieve all running processes in all sessions (user processes, services, etc)

The command is as easy as:

tasklist /S remotehost

Remember you will need local administrator access for the remote computer (i.e. domain admin). Then you can either start cmd.exe as domain admin, or add the credentials to the tasklist command:

tasklist /S remotehost /U domain\username /P password

Output will look like:

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