What have electrons, black holes and Clifford Algebra ever done for us?

Yes! Also, it is not the 'Planck Power'   (despite what you might have read in   Misner, Thorne and Wheeler, P.980).  The existence of black hole horizons implies a maximum luminosity (power) limit in General Relativity. Not even gravitational waves can escape a black hole . Consider an (almost) black hole made of light (this is called a  Kugelblitz )  sphere of radius $$\begin{equation} \notag R \geq \frac{2Gp}{c^3} \end{equation}$$   which is filled with photons with a total mass-energy of momentum $p$ times speed of light $c$ $$\begin{equation} \notag E=p \ c \end{equation}$$ that leave after a time  $$\begin{equation} \notag t=R/c \end{equation}$$   with average power (luminosity)  $$\begin{equation} \notag P = \frac{E}{t}=\frac{p \ c^2}{R}=\frac{c^5}{2G} \end{equation}$$ This is maximum power in GR , regardless of the nature of the system. You might be tempted to call this half a 'Planck Power' but there is no $\hslash$ in this expression, it is pu...