Hello Your Majesty!
I'd be happy to help. "Advocacy" is a pretty strong term. It describers a proponent or supporter of an act or cause who publicly declares their support for said cause and fights for its acceptance. I don't think the author ever goes so far as to declare their personal support for the multiverse hypothesis. Even the examples you give ("lead us to expect" and "
may well prove") are peppered with hedging terms like "may." I would definitely agree the author is open-minded to the possibility of a multiverse, and sees areas of evidence that support this idea. But I don't think the author ever goes so far as to say that they are convinced themselves and now are campaigning in favor of the hypothesis. Hope this helps!