There is no question that this stuff is hard (and has been cutting edge for decades) and that it is easy to make mistakes.

> give a more accurate explanation (that makese sense to someone who's never taken a GR class)

It's hard to know what level of understanding to aim for on HN. There are non-relativist working physicists here who somewhat casually read other areas of physics (and mathematics) here, for example, rather than e.g. physics SE or looking through literature reviews.

I'm guessing that you have done GR but probably not much with approximations like GEM, nor looked into the history of gravitational waves (e.g. the 1950s-60s work by Bondi with collaborators like Pirani) before the wide availability of powerful computers and observational support for the linearized theory. My goal here is not to nitpick you, but rather to offer a couple of references that might interest you or anyone who is quietly reading along.

> I think I was totally wrong re: Ricci curvature.

R_munu = 0 for one (uncharged) BH, and also for two. Charged BHs are different (Reissner-Nordström's Ricci tensor is R_munu = +- g_munu r_{Q}^2 / r^4 where r_{Q}^2 = \frac{Q^2G}{4 \pi \varepsilon_0 c^4} and ε_0 is the electric constant, all thanks to the electromagnetic stress-energy tensor; the Ricci scalar remains 0).

Superposing two Schwarzschild or Kerr solutions is messy [Krivan & Price 1998 Phys. Rev. D 58, 104003 was a nice overview arxiv html5[*] <https://ar5iv.labs.arxiv.org/html/gr-qc/9806017>, 'two locally Kerr holes, no matter how close they are, will not superpose into a single Kerr hole. Though [this] "failure" of the close limit is physically correct, it is inconvenient [for doing perturbation theory]'] but doesn't change Rmunu = 0.

A charged binary is beyond the scope of this comment.

> I was thinking "oh, GW carry energy ..."

I can recommend two really good papers written at very different times.

Weber & Wheeler 1957 <https://journals.aps.org/rmp/abstract/10.1103/RevModPhys.29....> (it's also on sci-hub) where they struggle with the question of the sense in which GWs are real ("the only well defined way there is to express the influence of [gravitational] radiation [is] in terms of its effect upon invariant space time intervals betwee two test bodies"). I enjoyed seeing the rare \dotequalsdot in eqns 28,30, "geometrically equal to". Also, they lead right into the next suggestion with, "Similarties between gravitational and elecgromagnetic waves thus make it simple to draw a number of reasonable inferences. The significance of these inferences has a much more subtle character in the gravitational case than in the electromagnetic case. Neither field densities nor test particle motions have a meaning independent of the choice of coordinate systems. The simple observable consequences of wave action are instead changes in the separation of nearby test particles -- changes that are related to the covariant components of the curvature tensor R_ijkl."

Goswami & Ellis 2021 <https://iopscience.iop.org/article/10.1088/1361-6382/abdaf3> arxiv html5[*] <https://ar5iv.labs.arxiv.org/html/1912.00591> with the somewhat stentorian title "Tidal forces are gravitational waves". It is really about the Weyl curvature in binaries. The authors explicity consider (for orbital motions of two massive bodies) a decomposition of the Weyl tensor C_abcd into an electric and magnetic part (for which see §III; and eqn 6 repeats the point on R_ab in vaccum), the former compared to Newtonian gravitation and the latter being general-relativistic and encoding the gravitational waves that do not arise in the Newtonian theory. Their focus is on the magnetic part of the Weyl tensor, since (they argue) that is where all the interesting stuff is encoded, and how energy gets from the orbital system to an observer and between the binary partners themselves.

One highlight is a short paragraph summarizing some ~1960 work by Bondi and MacCrae [**], "Through a series of shape changing operations ... one sees that after each rotation, Tweedledum is gaining internal energy as the external tidal force is doing work on him, while Tweedledee is losing energy as she is doing work against the external force. This is an excellent example of how the internal energy of a system can be transferred to another system via gravitational induction, in Newtonian gravity." [emphasis mine].

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[*] lost way downpage and heavily downvoted is a HN user pointing out that the page of cartoons linked at the top is not accessibilty-friendly. I accept the point, and make up for it a little with the html5 links here. One can straightforwardly paste the trailing element of the ar5iv into a search engine or whatnot in order to reach a PDF version of each arxived paper above.

[**] The actual Bondi & McCrae paper(s) is(are) proving a bit elusive, but this gives a good overview: §§3-4, Tweedledum and Tweedledee and Energy Transfer (the latter starts with an excellent quote from Bondi in 1957), https://link.springer.com/article/10.1007/s10701-022-00660-z (open access). So this quickly became three papers, and I'll stop now, because I'm fairly sure you can find your way through them if you really want, and figure out how to get help if you get stuck.