I happened to speak to an NUS student a few months ago. The following were my takeaways
1. Recruitment is mostly centered around SE Asia. The Singapore work permit is quite competitive to bag.
2. MBB can be extremely hard to convert, especially in Singapore. People who convert, generally start out of offices in places such as South Korea and in lesser instances Hong Kong
3. Traditional Product Manager are few and far between at organisations like Microsoft or FAANG. Dell (or HP, Don't remember exactly) was probably the most known "tech" org hiring PMs. Most of the folks recruit into General Management/Leadership Development Programs type positions at these orgs. Most of the tech PM jobs tend to be at South East Asian based organisations like GoJek
4. Big push on FinTech and FMCG.
Now these are perspectives of only a couple of students. I would urge you to contact students to get a more accurate assessment.
S4G Nikhil anyone else, please feel free to correct/add
Posted from my mobile device