So i was also questioning this and did some research and i came up with something that im not sure is correct
Electron flow is the reason the LED lights up the fades but nit electrons that originated from the battery, but rather from the metal plates located inside the capacitor
keep note the series circuit is not actually closed, the capacitor has dielectric material keeping the current from flowing through
Before anything, both plates inside the capacitor are neutral, but ones you connect the battery, the electrons from the plates get attracted to the positive side of the battery. and that its self is current(flow of electrons)
so in conclusion, when the capacitors plates change in polarity, and electrons leave one of the neutral plates, those electrons create current lighting up the light but the plate doesn't have a lot of electrons so eventually the neutral plate loses most or all of its electrons making it positively charged and the other plate negatively charged and that's why the LED lights up then slowly fades when the current stops flowing