Ask HN: How valuable and useful are Professional Certificates?

Let's say one has been feeling stagnant in their career lately and wants to break into an adjacent field. For example, say a software professional wanting to get into AI. Assume they've already done a relevant undergrad degree.

Various reputable universities seem to be offer Professional Certificates in relevant topics, many of which can be done online, getting around geographical constraints - often the costs are more approachable too. The courses themselves are the proper university courses for the topic, just offered online. Complete a prescribed handful of them over a year or more, and you get a Professional Certificate in said topic.

Are these Professional Certificates worthwhile? We can discuss this from both a substance basis, in terms of knowledge and skills gained, but also from a 'real world results' basis, in terms of enhanced career prospects. Also, we can consider a specific example (though I'm interested in the general view as well), such as the 'AI Professional Certificate from Stanford University' or similar.

As a bonus question, how would such a Certificate compare as opposed to doing a full Master's program at a second-rate school?

Would love to hear your experiences and opinions, both from Certificate holders as well as employers and hiring managers who have come across these.