In the earnest interpretation of your question that presumes you're not trying to drag this into a quagmire of nitpicking over the metaphor, the analogous part of the California law to the casserole ingredient advertisement is announcing the user's age bucket to the world. The world being, any app or website that happens to ask for it. I don't know why you brought browser histoy into this, it's not in the law and I didn't mention it.

Anyway, the whole point of the metaphor, because I feel like I will have to explain it, is that we don't put these onerous "required labeling" rules in place for private individuals going about their own lives. So just like you don't have to tell anyone who asks what you put in your dinner last night, private individuals should not have to tell anyone who asks (websites, apps) what age demographic they fall into.

Note: this is one of many arguments I endorse against this type of law. This shouldn't be interpreted as "so that's all you're worried about?" just because we dissected it in detail here.