That’s not really the question. I could claim authority of you and your family. But what is the mechanism that enforces it? Why would you recognize that?
Why would Microsoft listen or care about the ruling? It’s because they operate in the UK. The CMA can’t just regulate companies that don’t operate in the UK.
if the companies' activities affect competition in the UK then the CMA is responsible.
the hint is in the name: Competition and Markets Authority