Imagining I had the money, should I buy an old HDB flat, renovate it and lease it out for a potential rental that will cover the entire cost of the flat and renovation?

Yeah reno of 300k quite a lot. also, it depends if you are paying all in cash or taking a loan (internet may be quite high now).

You had better check the restrictions on rental as well as your rental yield before you make that deduction. The yield on Singapore properties are not as high as they seem due to frictional costs on ownership. If you want liquidity with less restrictions but exposure to real estate focused in Singapore, a REIT is a better investment. The ongoing cost of a loan will be a big unknown factor as well if you go for a floating rate loan.