That was interesting but I’m not sure it answered the question? Was the answer that they don’t “time freeze” at the threshold of event horizons touching each other, but instead “pucker out” to meet each other?

I agree the wording in the article isn’t too clear, maybe a bit oversimplified.

One thing to keep in mind. What we see as the black hole is really the “event horizon”. To a local observer there’s nothing special at that location. You wouldn’t notice anything crossing it.

So really as the black holes merge, we see their event horizons merge. It’s not really valid to say one horizon falls into the other, as they are simply space time points like any other.

What happens to the singularities is probably a whole lot more complex and I don’t know if it’s well defined. In addition, there’s a lot more typically going on around most black holes since many have accretion disks of materials accelerated at relativistic speeds and are also rotating causing other gravitational complexities.

Where I think the article hits the nail on the head, is we need complex simulations and ultimately more data on observations to create more accurate models.