Don’t people have data caps where they’d notice if a ridiculous amount of audio was sent to a server?

If you did all of the analysis on device, even quite cheaply, you could just transcribe key words and phrases into a text file and upload that. That would only be a few kilobytes of data tops per day of unique words and phrases, I should think. And if you've ever tried to monitor data usage on an Android phone, you'll know that the monolith of Google Play Services phones home all the time with all kinds of pings and datapoints, so it wouldn't be hard at all to upload that data.

and you'd have no battery inside an hour.

watch words are simple to listen for, generalised transcription is far harder.

Doesn't your phone stay on charge sometimes?

There are a lot of people at this company, and my news feed doesn't diverge enough to account for all of their varied google searches.

No, but it would be easy to tell that you associate with your co-worked by correlating Bluetooth beacons, which many apps do for exactly this purpose.

More realistically, your co-worker googled it on their phone. They also email/chat/sms/call you once in a while, so they know you're connected.

Now, it's only logical that you may share certain interests, so why not show ads for things they bought/googled for to their contacts?