There's a whole design niche dedicated to making that label as subtle and hard to see as possible.

And I'm skeptical ads will remain outside of the ChatGPT output for very long. You can hide a div tag, but you can't hide an advertisement streamlined into the "conversation" with ChatGPT. Is ChatGPT recommending product X because they're an advertiser, or because that's what it "learned" on the internet? Did it learn from another advertisement?

I fully expect them to exploit the plausible deniability.