Monitoring and Alerting Specific Scheduled Task on multiple Windows Servers

If you want to monitor specific scheduled tasks, powershell SAM component would probably be your best bet.

To filter, you would probably just swap out this:          "FALSE" {$SchTask = Get-ScheduledTask -ErrorAction Stop | Where-Object {$_.TaskName -notIn $Exclusions}}, to be an In instead of notIn.

Then you could just provide a list of schtasks you want in the script argument line (comma seperated list)

#Build Exclusion List
    If ([String]::IsNullOrWhiteSpace($Args) -eq $False) {
        $Exclusions = $Args
    }

#Retrieve Scheduled Tasks
    Try {
        Switch ([String]::IsNullOrEmpty($Exclusions)) {
            "TRUE" {$SchTask = Get-ScheduledTask -ErrorAction Stop}
            "FALSE" {$SchTask = Get-ScheduledTask -ErrorAction Stop | Where-Object {$_.TaskName -notIn $Exclusions}}
        }
        
    } Catch {
        Write-Host "Message:  Error running scheduled task $($Error[0].Exception)"
        Exit 1
    }

#Display State Count
    Write-Host "Statistic.StateReady:  $(($SchTask | Where-Object {$_.State -eq "Ready"} | Measure-Object).count)"
    Write-Host "Statistic.StateDisabled:  $(($SchTask | Where-Object {$_.State -eq "Disabled"} | Measure-Object).count)"
    Write-Host "Statistic.StateRunning:  $(($SchTask | Where-Object {$_.State -eq "Running"} | Measure-Object).Count)"

#Detect Failed Jobs
    $ActiveTasks = $Schtask | Where-Object {$_.State -eq "Ready" -or $_.State -eq "Running"}
    Try {
        $ActiveTasksInfo = $ActiveTasks | Get-ScheduledTaskInfo -ErrorAction Stop
    } Catch {
        Write-Host "Message:  Error running scheduled task info $($Error[0].Exception)"
        Exit 1
    }
#Results
    Write-Host "Statistic.ResultSuccess: $(($ActiveTasksInfo | Where-Object {$_.LastTaskResult -eq 0} | Measure-Object).Count)"
    Write-Host "Statistic.ResultError: $(($ActiveTasksInfo | Where-Object {($_.LastTaskResult) -ne 0 -and ($_.LastRunTime -gt (Get-Date).AddMonths(-1))} | Measure-Object).Count)"
    Write-Host "Message.ResultError: $(($ActiveTasksInfo | Where-Object {($_.LastTaskResult) -ne 0 -and ($_.LastRunTime -gt (Get-Date).AddMonths(-1))}).TaskName -Join ",")"
    Exit 0

How to implement the PowerShell script to the Nodes that are already added to the SAM?

You would need to create a powreshell monitor in SolarWinds, utilizing the code:  Create a Windows PowerShell script monitor in SAM

Then you would need to add the template to the node:  https://documentation.solarwinds.com/en/success_center/sam/content/sam-managing-templates-sw1127.htm#Assign

You would need to create a powreshell monitor in SolarWinds, utilizing the code:  Create a Windows PowerShell script monitor in SAM

Then you would need to add the template to the node:  https://documentation.solarwinds.com/en/success_center/sam/content/sam-managing-templates-sw1127.htm#Assign