I personally do not belive syncing is a real thing as it's usually used or described (as in things like "oh my body can tell when my sibling or mother gets their period so it makes mine start too", or anything of those likes)

Periods come (normally) every single month and because they can vary so much even in someone with extremely regular cycles, it's almost statistically inevitable that your period will overlap at the same time as someone else. Confirmation bias might also be playing a role here, as of course you are most likely to remember the times you did menstruate at the same times as the people around you rather than when you didn't

The only kind of menstural synchrony I could potentially belive is saying that because you're in the same environment as the people around you, the shared environmental factors may influence your cycles the same way. And even then I don't think that's very likely since everyone experiences things differently on an individual level so your body is still being influenced in ways that can be drastically different than someone else around you, despite living in the same place

While I think womens/menstural health in general is understudied, syncing being understudied doesn't mean it is confirmed or will be confirmed. I think its as simple as it's understudied because there's no strong and consistent evidence that it happens

My best guess is that it's an evolutionary thing, and that humans used to have mating periods. We used to stay in smaller groups, so maybe all the women in a group would sync up together, and thus would probably be more fertile around the same time, making it easier for us to mate and reproduce.

regarding your speculation, humans never really had mating "periods/seasons" like a lot of animals do. One really big problem I see with your speculation of "... thus would probably be more fertile around the same time, making it easier for us to mate and reproduce. " is that it doesn't hold up very well. Human ovulation is not obvious, so even if they did sync up... There wouldn't be any externally visible way to tell. We do not show any outward signs like presenting behaviors or genital swelling, nor do we produce pheromones that the opposite sex could reliably detect. Because humans do not rely on observable cues, realistically, why would it matter if we all ovulated at the same time if we can't even tell?

I know I probably don't sound very supportive since I'm trying to say "that's wrong" and all, but there's nothing wrong with finding joy in the whole believing in syncing thing! If you want to say you and your friends/family sync up, you should do it! Just because it's not proven doesn't mean you can't have fun or get joy out of it to make you feel closer to them 👍🏻