Many people really forget how brutally poor Singapore was not long ago. After being kicked out of Malaysia for wanting equal racial rights they had no land, resources, army or wealth. Any reasonable assessment would project them staying third world for a long time.
As boomers were entering adulthood in 1970, the GDP per capita in Singapore was US$900, in Australia it was $26,000.
Australian pensioners are the wealthiest of that cohort on the planet. Due to rampant property gains and incredibly favourable tax laws, technically you can live in a $10M mansion and still collect a full pension + benefits.
The two countries took wildly different trajectories and as such have very different attitudes by the generations that grew up in that time.
For a thousand dollars or so you can get setup and run your own hawker stall a couple hours a day in Singapore, lower that cost to a few hundred if selling sundries. The only equivalent I could think of for Australians is weekend markets which are full of oldies, but those are transient tents on some grass which are usually quite competitive to get and are once a week/month things.
Undoubtedly there's many who do need the income even in old age, but there's also a big cultural difference and many don't really consider retirement a thing. They may work a lot less, but have no plans to stop until physically unable, this is pretty common attitude to see.