When you say a bolt lasts 30μs, that’s about the time for one ‘surge’ of electrons to jump through the air, but that isn’t the thing we see. Electrons, even trillions of them at once, are invisible.
When that surge happens, it heats the air along its path glowing-white hot (as the flowing electrons crash into air molecules), and that’s the part our eyes detect. The air remains hot, and visible, for tenths of a second even though the electrical event that heated it is over.
Another thing to think about is, a lightning bolt is usually not just one electron surge. After that first surge, the heated air is more conductive for a while (IIRC due to extra ions created by the first surge) and so it’s easy for a few more surges to jump along pretty much the same path. Every one of them re-heats the air, keeps it glowing, and keeps the bolt path visible to our eyes.
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