What's the value of Coursera certificates to one's career in Singapore?

It helps a litte - especially so when you add it under the "Skills" section. Else you can always mention that you did a certain course on Coursera during the "walk me through your resume" segment and use it as a topic for discussion.

If you're coming from a purely learning perspective, then there's different ways to upskill besides Coursear. For e.g., SkillsFuture or LinkedIn Learning (provided by my school) and those have certificates too. You can also go directly to the company you're interested in (for e.g. Google Academy, IBM Design Thinking, AWS Cloud computing etc.) for specific courses that you're interested.

Personally I think Coursera is better than Udemy as Coursera offers programs from accredited institutions, courses can be taught by only educators, experts, and professional instructors and certifications are given by the name of a professional institution... the list goes on

I can't speak for employers, but I imagine that the certificates give legitimacy to what you have learned, and there are some courses on Coursera that are quite well-known; It adds credibility to what you say you learned or did outside of work in your resume/CV/interview.