It's not. Even in Newtonian mechanics kinetic energy is an observer-dependent quantity; in General Relativity we care about the stress-energy-momentum tensor, and you can slice that up into kinetic and potential energies as you wish by applying coordinates.

The vast majority of the stress-energy in the immediate neighbourhood of an accreting black hole formed by stellar collapse is found inside the horizon, even if there is a substantial accretion structure.

General Relativity doesn't make any predictions about the forms stress-energy-momentum can take; we get that from matter theories like classical (but relativistic) Maxwell's equations, quantum electrodynamics, or the full Standard Model. (One also runs into "toy" or "test" forms of matter -- various idealized space-filling fluids or dusts, mainly, that approximate matter in the large: huge numbers of stars or huge numbers of galaxies, for example). So General Relativity also has nothing much to say about kinetic energy vs potential energy: just that they each must contribute to the Einstein Field Equations and that typically means being encoded in the stress-energy tensor.

The perfectly elastic bouncing of microscopic particles of a gas each bouncing in one dimension between opposite sides of the inside of a gas container produces a beautiful relationship between the kinetic energy of a gas and its pressure. https://en.wikipedia.org/wiki/Kinetic_theory_of_gases#Pressu... (PV = 2/3 K)

Assuming isotropic pressure at time t, we encode an identical contribution into the pressure components of the stress-energy tensor (the green diagonals here https://en.wikipedia.org/wiki/Stress–energy_tensor#/media/Fi... ) for every point within the gas cylinder.

The inner regions of massive stars have a lot of pressure; collapsars like neutron stars have even more pressure deep within them. In a runaway collapse that leads to the formation of a black hole, pressure typically dominates the stress-energy tensor, driving the formation of the event horizon.

By contrast, a Schwarzschild black hole is a vacuum solution of the Einstein Field Equation, meaning that the stress-energy tensor is everywhere zero. Thus there is no pressure. The source of the "central" mass inside the horizon of a Schwarzschild is best thought of as gravity self-gravitating, or if you like, "it's just defined as curvature alone until you throw a test object in".

If we perturb the Schwarzschild black hole by throwing neutral test objects through the horizon, the stress-energy tensor inside the horizon must be somewhere nonzero, but once through the horizon (ignoring quantum effects) the nonzero stress-energy stays in there, and everywhere outside the stress-energy tensor returns to zero.

An astrophysical black hole by stellar collapse locks up stress-energy in the same way: once it's inside the event horizon, it stays there (ignoring quantum effects, principally Hawking radiation). Stress-energy outside the horizon might cross the horizon in various ways, or it might form some long lived arrangement sufficiently far from the horizon. You wouldn't say that a white dwarf partner in a white-dwarf/black-hole binary forms "the kinetic [or other] energy of a black hole", would you? If not, then neither does any matter near -- but outside -- the horizon.

The no-hair theorem(s) mean(s) that in general you cannot distinguish between an uncharged, zero-angular-momentum black hole formed by stellar collapse (or black hole mergers) and a Schwarzschild (vacuum) black hole (say, formed primordially from nothing but gravitational radiation), even in binaries. A binary of uncharged, no-angular-momentum black holes may be two Schwarzschild BHs or two astrophysical BHs or one of each. The momentum-energy that leaves the binary cannot come from the stress-energy tensor of a Schwarzschild black hole, because it's zero everywhere in the horizon. If no-hair is true, it can't come from the stress-energy tensor in the interior of a black hole formed by stellar collapse, either. A very large primordial BH will have had a bunch of things fall into it (if nothing else, lots of CMB photons), but can still have essentially no stress-energy inside. Primordial black holes are not especially crazy: that's one possible way to explain supermassive black holes ( https://en.wikipedia.org/wiki/Supermassive_black_hole#Format... and note it's possible that primordial black holes can start with and retain essentially zero angular momentum).

A pair of primordial SMBHs, each near the centre of mass of merging galaxy clusters, may have eaten a bunch of stellar masses worth of dust and gas in their lifetimes, but not nearly enough to account for the gravitational radiation that will be emitted late in their inspiral, let alone during the merger and ringdown. Instead, it is the angular momentum of the binary system (as a whole, since in this sketch neither BH rotates) that must power the gravitational radiation during the inspiral.