So i was also questioning this and did some research and i came up with something that i'm not sure is correct
Electron flow is the reason the LED lights up then fades
but not from electrons that originated from the battery, but rather from the metal plates located inside the capacitor
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 once you connect the battery, the electrons from the plates in the capacitor get attracted to the positively charged side of the battery.
and that its self is current(flow of electrons)
when the capacitors plates change in polarity, and electrons leave one of the neutral plates(p1) to go to the positively charged side of the battery and repelled from the negatively charged side of the battery, to the other neutral plate(p2), causing it to become negatively charged, those electrons create current, lighting up the LED.
but the plate doesn't have a lot of electrons, so eventually the neutral plate loses most or all of its electrons and the other plate gains electrons.
when one of the plate runs out of electrons, current flow stops , explaining why the LED eventually stops lighting
and then after you have charged your capacitor, one plate is has a lot of electrons(negatively charged) and the other has a lack of electrons so more protons(positively charged)
and they are both attracted to each other inside the capacitor, they are eager to "connect" or "touch"(for the lack of a better word)
but cant because of the dielectric material
so the only way for them to touch or reach each other is if the terminals are connected by some conductive material
so when you connect the LED to the circuit, in series, the electrons now have a way to reach the protons(positive plate)
so they flow inside the conductor, creating current
so when you put a load, such as an LED, current flows though, making the LED light up, but for a short while
then the 2 plates both reach a neutral state, ones the positively charged plate has gained electrons and the negatively charged plate has lost electrons. then the current stops, when the flow of electrons stop
i watched ElectroBOOM's video on capacitors and a few google searches
it helps with the understanding