> Counter-intuitive perhaps, you get smaller standard errors when you observe higher counts.

No, the relative error aka. std/mean decreases. For Poisson, var=mean=N => std/mean = sqrt(N)/N = 1/sqrt(N). I'm sure the author knows this but the post is not written very clearly imho. I wonder who the target audience is?

When I was a junior researcher I rather found confusing that variance increases with increased counts. But the perceived "error" is the standard deviation relative to mean, which does decrease as shown above.