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>without any residual longer-lasting effects

A massive ripple in the very fabric of reality?

Well it sounds like a massive ripple in the fabric of reality which passes by us in a fraction of a second, never to be seen again. So from my non-physicist point of view, no it doesnt seem like a very long lasting effect, relative to us at least. Thanks for the snark though.

You're left with a big-ass black hole...

There's a theorem that black holes have "no hair": two black holes of the same mass, charge and angular momentum are indistinguishable. So the merge must happen instantaneously: if the combined black hole were "sloshing" afterwards that would violate that theorem.

Whether or not black holes have "no hair" is currently an unsolved problem.

Hawking, for instance, believes that the Hawking Radiation from a black hole encodes the information that went into creating the hole.

https://en.wikipedia.org/wiki/Black_hole_information_paradox...