TDR is also something doable. As I recall, planes tend to look like ideal capacitors, with a tiny discontinuity basically due to TL-connector-board stubs (and by TDR, I mean like 20ps risetime, so this includes features like pads and vias!), and then an ideal capacitor after that.
Analytically, we can expect a via into a plane looks like an inductance of mu_0 h ln(R/r), where R is the radius to anything of interest (e.g. nearby via fence), r is the radius of the via in question, and h is the plane separation height. This is a few nH for practical values, so adds with the via, trace and component body inductances as we would expect.
The full-field version of this considers the via as a boundary condition, and waves propagate radially from it; eventually reaching other boundary conditions and reflecting or scattering off them (other vias, plane edge..). We can see intuitively that, as the wavefront propagates, its circumference grows proportional to time, so the impedance is reciprocal with time (which is to say, an inductive characteristic).
The impedance of this propagation mode is quite low, so even if it has poorly damped reflections, their effect won't be severe on the circuit. (The Q is also fairly low, say in the 10s, due to the losses of FR4.) Which we kind of see in the video: the peak at -40dB is still a mere 250mΩ. Not exactly stellar for a beefy FPGA or CPU, but more than enough for most MCUs and various RF application.
Interesting by the way, that the measurement changes significantly with capacitors installed, even at high frequencies. Probably, the fact that anything's connected to the via stubs, is what we can blame for this effect; that is, with them completely disconnected, waves are able to propagate relatively freely. It's not that the capacitors are irrelevant at high frequencies -- just that they aren't dominant. And, probably something like, those stubs will have modest AC resistance at such frequencies, so, even though those stubs are inductive up there, it's yet another source of losses.
Tim