As I use my Pipelines inside Job classes, I will follow you @hakre kind of.

My Pipeline steps will throw the exceptions which let the job fail and as a result the job "failed" function get called which finally handles the exception ,e.g.:

class GetLabelsV0 implements ShouldQueue
{
    use Queueable;
    use InteractsWithQueue;

    /**
     * The number of times the job may be attempted.
     *
     * @var int
     */
    public $tries = 1;

    /**
     * Indicate if the job should be marked as failed on timeout.
     *
     * @var bool
     */
    public $failOnTimeout = true;

    /**
     * The number of seconds the job can run before timing out.
     *
     * @var int
     */
    public $timeout = 180;


    protected InboundShippingLabelContainer $container;

    /**
     * Create a new job instance.
     */
    public function __construct(InboundShippingLabelContainer $container)
    {
        $this->container = $container;
    }

    /**
     * Execute the job.
     */
    public function handle(): void
    {
        //Add Job UUID to the container
        $this->container->jobuuid = $this->job->uuid();

        JobLog::create([
            'uuid' => $this->job->uuid(),
            'jobname' => 'CancelInboundPlan',
            'tablename' => 'inboundplans',
            'entryid' => $this->container->databaseID
        ]);

        $succ = app(Pipeline::class)
        ->send($this->container)
        ->through([
            GetLabelDownloadURLPipeline::class,
        ])
        ->then(function(InboundShippingLabelContainer $container){
            $updateDB = InboundPlan::where('inboundplanid',$container->inboundplanid)->where('account',$container->__get('account'))->update([
                'labeldownloadurl' => $container->labeldownloadurl
            ]);

            return $container;
        });  
    }

    /**
     * Handle a job failure.
     */
    public function failed(?Throwable $exception): void
    {
        if(boolval(env('APP_DEBUG'))){
            DebugLog::create([
                'function' => 'GetLabelsV0',
                'object' => json_encode($this->container,JSON_PRETTY_PRINT),
                'message' => $exception->getMessage()
            ]);
        }

        //SEND GET MESSAGE TO FAILURE WEBHOOK
    }
}