how do i delete an old brand youtube channel without killing the google account

if you're not totally sure, use the hide option on that same screen instead. it takes the channel and videos out of public view but keeps everything, so you can bring it back later. delete is permanent.

Switch into the brand channel first (profile picture > switch account), then in YouTube's settings go to the advanced settings and choose delete channel. Because it's a brand account, that only removes the channel, your personal Google account stays as it is. The bit that catches people: if you're still switched to your personal channel when you hit delete, that's the one that goes. Check the name at the top before confirming. And download anything you want to keep first, deleted videos don't come back.