Working from Ramhound's answer I have discovered the culprit. It is something called the Intel(R) Management Engine, which is just a rebranding of its old Active Management Technology. The difference is that AMT was previously an optional component on Intel-based systems, but Intel is trying to make IME mandatory. Currently, it appears you may be able to disable it, by disabling or removing the IME "driver", which is not actually a driver at all, but is application code running at a privileged level below the operating system.
This is a software feature implemented as a driver on Intel-based motherboards which allows Intel to back door into computers running the software to install new drivers, microcode and as of today, apparently, send ads to users.
Obviously, it is a huge security risk, and as I found out various hackers and "security researchers" are already publishing various vulnerabilities it has and how to use to hack any box running it remotely. To answer my own questions:
What is the spyware process doing this?
Intel Management Engine Interface
What information is being sent to Intel?
Unknown. Intel considers the types of information it transfers into and out of a box running the software to be secret and proprietary. At a bare minimum it includes a list of all the drivers the box is running, the motherboard type and version and configuration and the CPU ID. The data Intel sends to and from the box is encrypted, so it is not possible for a (non-hacker) to know what is being exfiltrated from their box.
Is the information being sent directly to Intel, or is Microsoft
collecting the information off the computer, sending it to Intel, then
relaying Intel's ad to me?
The information, including the content of the ad, is being directly sent to and from Intel.
it appears Intel is being notified of my "status" every time I boot my computer
. Uhh, what?! How do you figure? Nobody is sending anything to Intel.