I didn't know that the two-capacitor paradox was a thing until 2003 when W5OLY asked me to run some Spice simulations for a letter he was preparing for QEX magazine.  (See Wikipedia here )

It all came back to me when I bought the 2024 book by Paul J. Nahin,  The Mathematical Radio, inside the magic of AM, FM, and Single-Sideband.  The book opens with the two-capacitor problem and electromagnetic radiation.  I groaned at first, but as I read on, I realized Nahin both reveals the limitation of the puzzle, and presents a much more historically interesting circuit, the RLC resonator.

Re-simulating with QucsStudio led to a much longer excursion than I expected, which is documented in the slides below.  The simulations in 2003 were done with PSpice, and used the PSpice switch component, S.  After putzing with switches ( here ), I discarded the switch, and used an initial condition voltage on the capacitors, instead.