I do not think there is a cut off age for residency in Singapore. I have seen ppl in their late 30s doing residency. However, I would say most starts about 27-30?
If you follow this forum, you would see that 'most' of the time, the argument is about money vs passion and by passion it means to pursue sub-specialty training. Will you be at a disadvantage coming back at 31 to start medical career? The answer is probably no; provided you are able to shine or integrate fast, because sometimes, getting into residency is as much about knowing the people and system as being an outstanding medical officer.

I don't think i can advise you on medicine vs engineering. It is two vastly different work and pathway. However, if you are someone who enjoys and opens about working with different people and in different countries, maybe engineering is better because i believe it is not that strict to work in other countries with engineering degree than a medical degree due to licensing issues.

Hope this helps! Good luck!