What are you disputing about the explanation given in the post? As far as I can tell, it’s basically accurate (although the pendulum unit was called the toise, and the meter seems to have targeted half a toise). If you accept that account, it’s not a coincidence.
I initially had an objection due to a misconception I was carrying.
I see now that the pendulum formula is a pure relation between time and distance/length. It will apply regardless of the units used. For example if we measure time in fortnite and length and furlongs the formula will be the same. The gravitational acceleration of course will be in those units: furlongs per fortnights squared. Needless to say that will not be 9.81.
Now the meter unit was chosen in relation to the second unit by the length of a pendulum that produced an integer period. So that choice/relation caused the gravitational acceleration g to take on such a value that its square root cancels out the π on the outside of the root.
I was confused for a moment thinking that the definition of the kilogram would somehow be mixed up in this but of course it isn't. g doesn't incorporate mass; and of course pendulum swings are dependent only on length and not mass.
There are all sorts of situations in which certain units either give us a nice constant inside the formula or eliminate it is entirely.
For instance Ohm's law, V = IR. It's no coincidence that the constant there is 1. If we change resistance to some other unit without changing how we measure voltage and current we get V = cIR.
