> Do people just let "claude take the wheel"?

Yes, I'd wager most people just let "claude take the wheel".

> When you have to go in to your next standup and explain what your code does to your boss, and what you've done since the last meeting, what do you say?

You say "Claude, I've got a standup in 10 min, give me a high level summary for my boss of everything you did since the last standup" and then you read that lol.