But you only get two, because all you have is a stone-age society. Your two conditions:
20% of a given population dies each year. (There's also a high birth rate, so overall population tends to not decline year over year.) This means that after two decades, almost all the population from a given year has died.
The act of recording events, or reviewing those records, involves thinking (gasp), which can trigger new and unusual supernatural events around the offending party. These events have a tendency to destroy the records, the offender, or both, so maintaining a written history of the world is difficult.
...make any form of technological advancement other than by sheer, unadulterated luck impossible. Maybe... maybe... they have picks. But anything beyond that is unbelievable unless you've written a whomping good story.
So, what are your two holidays and/or celebrations?
It's theoretically (if not practically) possible for stone-age peoples to mark the passage of a year with enough accuracy (but not precision) to have a "birthday" style celebration. And in your society, the ability to make it another year is a big deal.
And, by definition, anyone living in our
Logan's Run-esque society run by teenagers young adults would be absolutely amazed that their palm crystal turned black they passed their 20th birthday. Such people would be heralded as the wisest-of-the-wise.
Now for a frame callenge...
You haven't told us a thing about your indigenous people. That leaves us assuming that they're basically human, which might be completely in error. One hopes this is the case, because...
While there's more than ample evidence that teenagers can raise babies, the reality is that without what we, millions of years later, would call an "education" they're basically spending their whole lives and effort gathering food and raising the next generation. While every 15-year-old believes the following statement to be absolutely false, the truth is that teenagers are not small adults. They're dying before they are physiologically, mentally, and emotionally mature. This is why they're stuck in the stone-age. They're animals. They don't even have the time to develop language (much less holidays).
Your indigenous people are literally incapable of developing any advancement in technology. They die too fast for even the most rudimentary technologies to spread far enough that they can be "remembered" by people over such a short time span. Like you said, no written records. And it doesn't help when the shovel in your hand is suddenly possessed by the idea "FREEDOM" and starts beating the snot out of some poor unsuspecting not-going-to-be-a-15-year-old.
That means that even the two celebrations I mentioned are unlikely to ever take hold. If, left alone, would a 10-year-old come up with the idea of celebrating a birthday? I doubt it. I doubt it would even come to mind until someone turned 13 or 14 — by which time they've lived 70% of their lives. Even religion is unbelievable as most humans don't start developing faith or questioning the faith of their parents until more-or-less age 15, by which time they're mostly dead. There's literally no time to develop a religion, must less codify it such that a celebration could be identified (remember "holiday" comes from "holy day").
The basic story of Logan's Run works because someone else, a society much more technologically advanced, developed all the underlying science that allowed for an enclosed, self-supporting world that didn't depend in any practical way on the inhabitants actually knowing how anything worked. You appear to not have that situation. So... Stone age.
I doubt any celebration would be held at all. Your inhabitants are too busy gathering food, raising babies, and avoiding anthropomorphic shovels.
Unless your indigenous people are NOT human, in which case you can have any celebrations you want because you can develop the society any way you want and this entire question gets closed for being opinion-based. We can't read your mind.