Regarding the spooky coincidence effect: the truth is that people are a lot more predictable than they assume they are. More often than not, when you're doing a thing related to X and then 10 minutes later you see an X ad, it's because you're actually in the bucket of people who like X and the buckets are highly correlative. You might be in that bucket because you like Y and 95% of people who like Y like X, and a search for Y, followed by doing something related to X, triggered the X ad because of the Y search. There's also huge confirmation bias on those coincidence ad views; everyone has a story of one, but I've yet to meet anyone who said "I sat down and recorded every ad I was shown for a week. 90% of them correlated with an activity I was doing in an unrelated Google product between 5 and 10 minutes before the ad was shown."
I can absolutely see this happening due to their sheer size losing control as everything is probably silo'd and confusing.
Due to a tax issue last year, I urgently needed a specific from a former GIANT company I worked for per my accountant.
It took over 6 days of calling, emailing and getting transferred around the bureaucracy because they had recently outsourced that HR function to another company and moved all the data and the Director of HR for that entire 1000 person department couldn't even get me the form and didn't know what to do! She and I had to put in a ticket together to the help desk and eventually someone at the outsourced help desk escalated it enough that we found out the physical forms were actually in transit to the east bay offsite location and had not been digitized yet which is why they were not able to provide the form until a 14-business day turnaround.
It was the most absurd and frustrating experience and definitely made me happy I'd moved to a more midsized org. We might not be an industry Titan but at least are small enough to be functional and not get entirely lost in bureaucracy.
Of course, you could just as easily conclude that they're lying, but I find that harder to believe.
Everyone has some stories about how Google drew a suspicious correlation between products not supposed to be connected. In my case, there was one day where I wanted to watch an MP4 copy of Harry Potter I had on my NAS while on a work trip. Obtained ages ago. I uploaded it to my G-Suite Business Google Drive (not shared, nothing was pirated here despite ripping blurays still being a legal ish-zone). Later that day, YouTube started suggesting clips from Harry Potter to me.
Suspicious. Not damning. Are they scanning my Google Drive for filenames to feed to the YouTube recommendation engine? I don't know. Maybe it was just chance, or maybe a few days ago I clicked on a random article about JK Rowling's latest drama and that was enough to trigger three layers of indirection through the Google Brain and suddenly I love Harry Potter (I don't. Its fine. I'm sure after writing this out, though, Google's opinion on My opinion of it will be reinforced.)
But lets say I never watched those videos recommended to me. Is the YouTube recommendation engine data fed to their ad engine? What if I never click on something, but the system knows it presented it, and maybe I like Harry Potter anyway? I don't know. But it seems feasible, doesn't it? And if that's the case, then the data traveled two steps, where each step on its own is weird, but reasonably ok, but the two steps together look less ok.
We're really talking about the absolute cutting edge here; Google is building a brain processing exabytes of data. If you're in engineering; have you ever worked in a job where you felt like you knew how every part of the system worked? I work at a company with 10 people and I still don't feel that. Why would Google be any different? Teams talk to other teams. A middle manager two jumps up approves it. They get access to a database. Data travels around. An engineering lead at the top thinks they have a grasp on everything, a grasp spuriously assembled from reports written by people who themselves understand some non-100 percent of whats going on in their silo. Things fall through the cracks, it happens all the time, and in this case we're talking about buses of data so big that no one could even look at it all to verify what's in there is what they think is in there (and if they did actually have humans look at it, that'd have concerns on its own).
This is my pet theory: That the desires and realities of Google are so different that even what they say is untrustworthy because no one there knows whats actually going on anymore.