I finally found the correct platform ID in order to make SideCar work. I explained the situation to ChatGPT and it gave me a list of IDs to try. This was the list:
So in reverse pairs:
And while 07009B3E didn't work for me (as posted earlier in this thread), the second one did the trick. So 08009B3E it is.
There were other IDs in this thread that basically worked for me, but all of them caused my macOS to take minutes to boot, as discussed earlier. 08009B3E is the first ID that not only successfully enables SideCar, but also doesn't interfere with the boot process.
It blows my mind that an AI could solve this problem in seconds after trying so many different IDs without success. The strange thing is, when I search for "10900k 08009B3E" or something, there really isn't much to see. Which means there would have been absolutely no way for me to come across this ID.