Bimfred

Hate to disappoint, but it's far more than you could possibly imagine. You could dump the equivalent mass of the entire human civilization, every single person and everything we've ever made, on the Moon and it wouldn't have a noticeable effect.

Aren't the batteries and electric motors driving the grid fins at the top of the booster? That and the entire interstage are gonna get blasted with the thrust plume of three Raptors. Reinforcing them enough that it doesn't affect planned reusability targets could take a bigger bite out of the payload than they get from hot staging.

That said, assuming the booster doesn't get royally annihilated immediately, they'll surely do a thorough analysis on just how much damage the booster takes. Might be that hot staging doesn't work out for regular use, but they'll keep it on hand for launches that need every last bit of delta-V.

I think Soyuz boosters currently do hot staging, the interstage is open IIRC.

You are correct. I believe most Russian rockets have used hot staging. It may be destructive, but it works.

The technological developments that built modern civilization have always come with tradeoffs at the expense of nature. This is simply the next step on that path. It's unfortunate that it's necessary, but commendable that they're making efforts to minimize the impact as much as possible.