I’m not a rocket scientist, but I still don’t understand why they do that so-called “hot staging.” Seems to me the booster is still either attached or way too close to the upper stage that there probably is some sort of damage done to the upper stage when it ignites. Seems like there’s too much of a possibility of ignition shock wave damage to the upper stage.
They do the hot staging to keep the rocket momentum going. When they previously separated the first stage they would separate before the second stage lit their engines. This would cause the second stage rocket to start slowing down before they could light the engines.
By hot staging they can keep the momentum going thereby saving fuel. But they have to make sure the top of the first stage can handle the second stage exhaust.