In spite of their different dimensions, the numerical values of $\pi^2$ and $g$ in SI units are surprisingly similar, $$\frac{\pi^2}{g}\approx 1.00642$$

After some searching, I thought that this fact isn't a coincidence, but an inevitable result of the definition of a metre, which was possibly once based on a pendulum with a one-second period.

However, the definition of a metre has changed and is no longer related to a pendulum (which is reasonable as $g$ varies from place to place), but $\pi^2 \approx g$ still holds true after this vital change. This confused me: is $\pi^2 \approx g$ a coincidence?

My question isn't about numerology, and I don't think the similarity between the constant $\pi^2$ and $g$ of the planet we live on reflects divine power or anything alike - I consider it the outcome of the definitions of SI units. This question is, as @Jay and @NorbertSchuch pointed out in their comments below, mainly about units and somewhat related to the history of physics.