I have no special knowledge, but ya I think that coincidence without obvious causation might be the basis of magic (spirit, consciousness, meaning, etc). It's also the basis of quantum mechanics. Pauli and Jung noticed the uncanny similarities a century ago:
https://en.wikipedia.org/wiki/Synchronicity
Basically, science can only puts bounds on this stuff, it can't predict the outcomes of stochastic/emergent processes. Which is where I believe free will resides.
Which might sound like hand-waving, except that it's fundamental:
https://en.wikipedia.org/wiki/Quantum_indeterminacy
People have tried to explain away stuff like quantum entanglement and failed:
https://en.wikipedia.org/wiki/Hidden-variable_theory
Basically it comes down to: either the quantum decision was made before the experiment started and stored in hidden variables, or there's a nonlocal connection over a 4th space dimension which we don't understand, or the quantum way of talking about these things is the only description that works. Which unfortunately (fortunately?) seems to be the case. Maybe someone who groks this can explain it with better words. My gut feeling is that this is the physical manifestation of incompleteness:
https://en.wikipedia.org/wiki/Gödel%27s_incompleteness_theor...
Anyway, I'm starting to believe that macro-scale effects like social interactions follow the same rules as quantum mechanics. Probably what we'll find is that it's waves and energy all the way down. Like if every person is an antenna, and our interactions play off one another in a vast multidimensional space we aren't aware of, like ripples on a pond. I suspect that this is what's going on inside atoms, and a real-world effect of this is that quantum computers will be limited by noise, and building a simulation of the Hamiltonian and running it would give the same result as flipping coins a bazillion times. This might be yet another hidden variables interpretation though so I'm almost certainly wrong. Probably.
In my own life, I mostly journal any synchronicities, which tend to happen about every 5 days for me, then weeks or months of nothing. I have about 50 written down, but feel that I've only caught maybe 10% of them.
In the last entry, I wore a bowtie to an event to try getting outside my comfort zone, then we came home and the TV was showing the scene where he makes the guy with the goldfish and bowtie leave the office in Wolf of Wall Street. Now what are the odds of that, since I've never worn a bowtie before and may never again?
I've had more intense happenings like that, but unfortunately a lot of them are negative around tragedies so I don't want to get anyone down. Mostly bad feelings before bad things happen. I think that has a lot to do with my disposition, so I've started watching more for angel numbers, and more love-based synchronicities, which seems to help. I believe that our sensitivity to the quantum chaos foam or whatever it is gets more attuned the more we tune out, dissociate, meditate, etc and turn the volume down on our egos. So anyone can do this stuff at any time, it's just that western culture doesn't really have a place for it yet.