I can’t say what the whole world thinks, but I can say what some people think; namely, people in Germany, UK and USA where I had interactions with the people there.
The Germans make the least assumptions. They don’t pretend to know. In part because we are not in the daily experience of most Germans. So they either know or don’t know. But there is general information that causes them to look at Singapore as a prosperous nation with significant abilities. They do not focus on the supposedly strict laws in Singapore. I think the Germans are much more disciplined than we are, and our laws are nothing to them. Generally, Singapore is well-respected.
The British know about Singapore because we were a British Colony. But their information is sketchy. They don’t know where Singapore is located, and often confuse us with Hong Kong. At that level of knowledge, their view of Singapore is invariably skewed. There is general respect because they hear from time to time that Singapore is doing well. This is a respect from Singapore’s prosperity. The British still carry around them a sense of superiority as the former masters of the British Empire and don’t really bother to know about Singapore.
The Americans think of Singapore primarily as a place that has strict laws, and that we cane people for the slightest infractions — like chewing gum (which we don’t). The vast majority like the strict laws of Singapore, and wish America were stricter. They are not as aware of Singapore’s economic prosperity or political influence. At some point, they may learn that Singapore is an American ally and are pleased the not everyone hates America. The recent movie “Crazy Rich Asians” has changed their view of Singapore somewhat. They now tend to overemphasize Singapore’s wealth. The media there report Singapore positively. Many Americans say they would like to visit Singapore. Singapore is suitably colorful to warrant a visit, and reported as being very safe, so there is no threat to life or limb. Many American politicians remain ignorant of Singapore and seem to think Singapore is somehow allied to China. Most times, Singapore does not come on their radar screen. For example, Singapore’s public healthcare is possibly the best in the world (imho) but no one pays any attention to see what Americans can learn from it. However, Singapore’s math syllabus has caught the attention of the Americans and some schools are implementing it. The problem with Singapore is that we don’t produce something that people use. (e.g. car, phone, TV, computers, etc). There is no product or brand association with Singapore and that keeps us out of their conscious thoughts. Those who deal with finance tend to know about Singapore because we are a financial hub. And even if they do not deal with international finance, the GIC acquisition of assets in America impresses Singapore on their consciousness. Again, it has to do with wealth. Singapore students who go to America may have good grades but they come across to other Americans as being bookish. Americans tend to be unimpressed by the scholars we send there.
Hope this helps a little. I suggest what people in other countries think of Singapore depends on who you interact with and from which country.
Edit. thanks for the upvotes. This is just a limited view from personal experience. I don’t expect the upvotes, but appreciate them. After the movie Crazy Rich Asians, and repeated media talk about rich Singapore, Americans are now more aware of Singapore at the popular level.