This is incorrect. You were correct with Google Cloud: While it's a market follower that can't even break the top three, it's definitely a non-ad-based business unit.
But Nest is, when viewed in a context that understands why most Google products exist. It should be obvious that Search exists to serve Ads. The first result of every search is generally an ad. That one's easy. Android and Chrome both exist to protect Google Search: They ensure that most people's default experience is to search Google for everything, so they get ads.
Nest is about ads, but you have to look at the competitive context. Apple, Microsoft, Google, are all shipping ecosystems. Large catalogs of products which interoperate best with each other. It's absolutely anticompetitive and most likely illegal, but that's a digression: The issue is that for Android and Chrome to protect Search to serve Ads is that people have to pick Google's ecosystem over other ecosystems. Sure, you can pick Apple's, and Google has paid Apple eleventy-billion dollars to still send you to Google Search, but they can change their minds at any time, and it's more beneficial for Google if they don't have to pay another company for your attention. Also sometimes Apple gets on a privacy kick and makes tracking users harder, which Google wants to do to sell ads better, so they gotta fight that too.
So the issue here is that Apple has iOS and then it has Siri, and then it has HomeKit, which all works very well together and provides a very clean unified experience. If Google didn't have an experience comparable to Apple's experience, people might leave Android for Apple, and that's bad. So products like Nest are entirely there to provide a Google ecosystem that is competitive to other tech companies' ecosystems, so that you view ads.
If not, how do you know that data from Nest isn't used to enhance your profile?
I mean: knowing the sounds or patterns of sounds (I'm trying to be generous here and not accuse them of actually using every word spoken near a listening device as input) or just the general pattern of temperature etc could be useful in figuring out what ads to show.
... on a less generous note they mostly don't need that data: their AI has already calculated that if you are a male at least you need to see even more ads for scammy dating sites or - lately - ads for pay-to-win games - possibly with female narrators that could also have been in the aforementioned ads.
Nest isn't exactly a profit center for Google though. Presumably it makes sense as a foothold into the smarthome/IOT industry which might become a big surface for ads and they wouldn't want to lose that opportunity (like how some companies have been late to web or late to smartphones to their detriment).
That's some very generous speculation. I'll grant you that ads is quite obviously (based on our public filings) profitable, but that doesn't mean every venture seeks to insert ads.
I don't think it's speculation at this point. It used to be about who could control the family room TV experience. Now it's about who can control not only the family TV, but also the whole ecosystem of smart devices in the home that you will interact constantly with such as voice assistants and those tablet/hub things. It's all for ads, they're already doing it.