Great idea. Thanks for your effort. I would eventually consider to make the status optional because sometimes you want to sync even archived or disabled entries to 3rd party libraries or do certain things independent of the status.

For isNewElement()…

• firstSave will only be true for non-draft, non-revision elements, so checking getIsCanonical() and !ElementHelper::isDraftOrRevision() in addition to firstSave are redundant.
  

  cms/src/services/Elements.php

  Lines 2438 to 2442 in 972d611

  	$element->firstSave = (
  	!$element->getIsDraft() &&
  	!$element->getIsRevision() &&
  	($element->firstSave || $isNewElement)
  	);

• firstSave will never be true when resaving elements via a resave/* command or ResaveElements queue job. Those will only resave existing elements (and won’t alter their state). So checking !$element->resaving in addition to firstSave is redundant.
• Passing the status into these functions wouldn’t save any complexity – if the calling code has to think about status, it might as well do its own $element->getStatus() === $status check.
• If you want to exclude propagating elements, you should be listening to EVENT_AFTER_PROPAGATE rather than EVENT_AFTER_SAVE, which will only get called once, after the element has been fully saved and propagated.

So that function is completely unnecessary. Just do this:

use craft\base\Element;
use craft\elements\Entry;
use craft\events\ModelEvent;
use yii\base\Event;

Event::on(
    Entry::class,
    Element::EVENT_AFTER_PROPAGATE,
    function(ModelEvent $event) {
        /** @var Entry $entry */
        $entry = $event->sender;
        
        if ($entry->firstSave && $entry->getStatus() === Entry::STATUS_LIVE) {
            // boom
        }
    }
);

And for isUpdatedElement()…

• All non-drafts/non-revisions are inherently canonical, so calling $element->getIsCanonical() in addition to !ElementHelper::isDraftOrRevision() is redundant.
• Same points about getStatus() and propagating as before.

Which leaves us with:

public static function isUpdatedElement($element): bool
{
    return
        !$element->firstSave &&
        !ElementHelper::isDraftOrRevision($element) &&
        !$element->resaving;
}

Which is slightly helpful, but only once you’ve taken the time to understand the very specific point of it, which feels like just as much work as adding a couple extra conditions yourself (or creating your own helper method).

Thanks. It's taken me a while to wrap my head around all the changes and break down my prior assumptions on how it had worked, but it's making more sense now. I've updated my answer on the SE thread to reflect these less redundant checks.