The rationale for the drug laws is interesting: when Singapore gained independence in the 1960s, it was essentially a small third-world city without much of a local economy.
Lee Kuan Yew realised that Singapore's future lay in becoming a trading city. They built a port, invested in infrastructure, and basically oriented all their policies around making the city-state as attractive as possible for foreign investment. One reason the streets were kept so orderly and well-maintained was to impress foreign visitors that Singapore was a reliable place to operate in (compare to many developing countries where the ride from the airport will pass ramshackle buildings, potholed streets, garbage everywhere, etc). They kept the British common law system because it's a good system to do business under. Etc.
They also knew that, given the region (SE Asia) is a hotbed of drug trafficking, if Singapore became a successful port then tons of drugs would pass through the city. Drugs would mean organised crime. Organised crime would mean corruption. Corruption would scare off foreign investment. Singapore could have ended up looking like most other third-world countries, only too small to retain its independence, and could easily have been reabsorbed into Malaysia or Indonesia.
The reason the drug penalties are so harsh is to scare away any possibility of drug trafficking happening there.
Just to be clear, I'm not condoning Singapore's policies. Weed is certainly not the same as heroin or crack cocaine. Harsh sentences for carrying a tiny bit of marijuana is pretty draconian. (I looked up some news articles, and it seems as though foreigners are unlikely to get the death penalty for small amounts of weed, but you can still expect jail time and caning.)
In a similar way, one rationale behind Singapore's censorship is a similar reason to the (effective) censorship many European countries have -- Singapore has some simmering ethnic tensions, and wants to prevent anyone publishing inflammatory rhetoric. (That's not the only reason, afaik, but it's one of them.)
Still: it's worth remembering that Singapore started out in an unusual position with unusual constraints. Everything they have done has been with the aim of turning themselves from a third-world to a first-world country in a few decades. They've seen many other post-colonial countries go down bad trajectories, despite said countries receiving tons of foreign aid, support from international organisations, allowing Western NGOs to operate internally, etc. So they don't have much time for Western journalists/academics/etc who push them to change their policies, because they think the policies they're being pushed to adapt would have led them to disaster.
If anyone's curious to learn more about the Singapore approach I'd point them to first look up Lee Kuan Yew's books, or interviews of him, to get an introduction to how he thought about governance and how he approached Singapore's challenges.
My own takeaway is that Singapore stands out because most other developing countries have been run so badly. It's not that Lee Kuan Yew had a brilliant political philosophy that all countries should adopt (he claimed to be skeptical of political philosophy), it's more that he was both pragmatic and took a long-range view, and put into practice many sensible policies that other developing countries could have adopted in an alternative timeline. On the other hand, that is definitely not to say that all of his policies are justifiable. I gather that Singapore is slowly changing now that they feel more secure in their first-world status, but they're still pretty averse to adopting the kinds of policies Western nations and the UN usually push other countries to adopt.