Inspired by all the answers I have put all the stuff together into one  Scripted Pipeline. Keep in mind this is not a Declarative Pipeline.
To get this example working you will need:
The idea I had was to abort the pipeline if it is "replayed" vs started by "run button"(in branches tab of Jenskins BlueOcean):
def isBuildAReplay() {
  // https://stackoverflow.com/questions/51555910/how-to-know-inside-jenkinsfile-script-that-current-build-is-an-replay/52302879#52302879
  def replyClassName = "org.jenkinsci.plugins.workflow.cps.replay.ReplayCause"
  currentBuild.rawBuild.getCauses().any{ cause -> cause.toString().contains(replyClassName) }
}
node { 
        try {
                stage('check replay') {
                    if (isBuildAReplay()) {
                        currentBuild.result = 'ABORTED'
                        error 'Biuld REPLAYED going to EXIT (please use RUN button)'
                    } else {
                        echo 'NOT replay'
                    }
                }
                stage('simple stage') {
                    echo 'hello from simple stage'
                }
                stage('error stage') {
                    //error 'hello from simple error'
                }
                stage('unstable stage') {
                    unstable 'hello from simple unstable'
                }
                stage('Notify sucess') {
                    //Handle SUCCESS|UNSTABLE
                    discordSend(description: "${currentBuild.currentResult}: Job ${env.JOB_NAME} \nBuild: ${env.BUILD_NUMBER} \nMore info at: \n${env.BUILD_URL}", footer: 'No-Code', unstable: true, link: env.BUILD_URL, result: "${currentBuild.currentResult}", title: "${JOB_NAME} << CLICK", webhookURL: 'https://discordapp.com/api/webhooks/')
                }
        } catch (e) {
                echo 'This will run only if failed'
                if(currentBuild.result == 'ABORTED'){
                    //Handle ABORTED
                    discordSend(description: "${currentBuild.currentResult}: Job ${env.JOB_NAME} \nBuild: ${env.BUILD_NUMBER} \nMore info at: \n${env.BUILD_URL}\n\nERROR.toString():\n"+e.toString()+"\nERROR.printStackTrace():\n"+e.printStackTrace()+" ", footer: 'No-Code', unstable: true, link: env.BUILD_URL, result: "ABORTED", title: "${JOB_NAME} << CLICK", webhookURL: 'https://discordapp.com/api/webhooks/')
                    throw e
                }else{
                    //Handle FAILURE
                    discordSend(description: "${currentBuild.currentResult}: Job ${env.JOB_NAME} \nBuild: ${env.BUILD_NUMBER} \nMore info at: \n${env.BUILD_URL}\n\nERROR.toString():\n"+e.toString()+"\nERROR.printStackTrace():\n"+e.printStackTrace()+" ", footer: 'No-Code', link: env.BUILD_URL, result: "FAILURE", title: "${JOB_NAME} << CLICK", webhookURL: 'https://discordapp.com/api/webhooks/')
                    throw e
                }
        } finally {
                echo 'I will always say Hello again!'
        }
}
Main trick was the order of lines to achive abort state:
currentBuild.result = 'ABORTED'
error 'Biuld REPLAYED going to EXIT (please use RUN button)'
First set the state then throw an exception.
In the catch block both work:
currentBuild.result
currentBuild.currentResult