Can somebody clarifies how qubes-update-check service works and how dom0 gets update notifications for TemplateVMs that are never powered on?

This is a tricky question, asking to answer from a belief standpoint more then a factual, empiric standpoint. That is, until proof given to infirm such claim that there is nothing malicious there through extensive reverse engineering, its either there or not there until it can be verified its not there. That is, the whole definition of a backdoor injection through either intentional wrong doing or negligence or both.

There is awesome reversing work that has been done in the past on older CPUs, showing some proof that hidden instruction sets were added into x86 in the past:

Remember the names on those papers and dig down that rabbit hole if the subject interests you.

But keep in mind that you cannot highly modify what is on die; you can only patch it, so introducing new instruction sets is not thought as being possible. But what one day was thought impossible is years later dismantled and proven untruth.

So here again, in the absence of open source code, readable and understandable by many, we rely on the reverse analysis of the few and decide to place our trust (belief) into either of the possibilities (trustworthy/untrustworthy) waiting for the evidence.