Sure. What's happening is, you have -- I assume some length of hookup wire, maybe a few feet, which has inductance, on the order of mu_0 = 1.257 uH per m of length. It's usually lower than this, by a geometry factor -- wires paired closer together, or broad facing sheets, have less inductance than loose wires, or loops or coils -- but it's in the ballpark.

So, say you have 1uH and you connect the battery to the RLC series circuit. L = 1uH, R is small (capacitor ESR, battery ESR, wire resistance, and C is whatever that capacitor is, apparently something like 22uF?

This is a transient problem, where the capacitor charges from initial zero, to battery voltage, through the L and R. R << sqrt(L/C) so it resonates and rings down. Voltage reaches a peak of 2 * Vbat in 1/2 wave or pi sqrt(L C) = 14.7µs, and the peak inrush current is Vbat / sqrt(L/C) = 56A or so, reached in 1/4 wave or 7.3µs, and every 14.7 thereafter (but decaying, as it rings down of course). (It'll be less than this due to resistance, though it's not clear how much; R is probably 10s of mΩ here, so it will ring for maybe a dozen cycles, give or take.)

Now, 24V would still be just within the rating of the device, though it's higher than you might've expected.

But we're missing one key point. The capacitor is nonlinear. You don't get 22uF in a chip that tiny, and have it work for any voltage.

This is where "high K" comes in. High-value ceramic capacitors are made with some blend of barium titanate and friends, which has an extremely high dielectric constant (~10k), but saturates easily (above a modest electric field, k drops precipitously). This isn't well covered in datasheets, you have to go looking for the characteristics. Example:

https://www.digikey.com/en/products/detail/murata-electronics/GRM31CC71C226ME11L/8323503Datasheet doesn't say anything about it. Gotta click through the SimSurfing link to see characteristics. It's -66% at 12V!

The consequence for our little RLC circuit is, at first the capacitance is large, which takes time to charge up, putting excess current into the inductor (~50A). Once voltage gets going, C drops like a brick and dV/dt goes way up. Consequently, peak voltage shoots up -- it's not going to be double the input anymore, more like 3, 4 times, or even more.

The regulator can't handle anywhere near that much, so it breaks down, and some amperes flow into it the wrong way. Needless to say it doesn't last long, and out comes the magic smoke.

So, by putting a TVS on there, the peak is simply clamped. The TVS is a beefy zener diode, which just holds the voltage ~constant when pushed above its breakdown voltage (not really constant, it has some internal resistance -- but a 5 or 10V range is a far sight better than without). It can handle lots of amps, so the peak current isn't a problem. The inductance just discharges into it a bit slower (over say 20 or 30µs) then the voltage settles down.

Another option is using "too big" of a capacitor, with some ESR -- an electrolytic, say 100uF 25V, with ESR ~ 0.2Ω. This will charge more slowly, limited by its own resistance (which is substantial compared to other resistance in this circuit), and while the peak current is higher (on the order of Vin / ESR) the voltage doesn't overshoot or ring. At least up to some maximum supply inductance (a few meters, because sqrt(4uH / 100uF) = 0.2Ω).

With illustrations:

https://www.analog.com/media/en/technical-documentation/application-notes/an88f.pdfTim