Catalysts work principally by lowering the activation energy of the reaction.

https://en.m.wikipedia.org/wiki/Activation_energy

They don't necessarily bring atoms or molecules together, per se, but some do.

Yes but activation energy is still a "system" level concept. It's not the actual atomic level mechanism that results in the reaction.

There are lots of different types of catalysts: Homogeneous (molecule, typically small, in solution), heterogeneous (solid or porous surface) and enzymes (biological molecules.) Many do work by bringing reactants together so that the relevant fragments can combine. Chemical reactions are usually described as going through an energetic transition state and many catalysts stabilize this state so that the reaction can "get over the hill" and become product. Of course, it also stabilizes it for the reverse reaction so the products can become reactants again. The overall equilibrium is not changed. Both reactions speed up. If, however, one extracts the product as it is formed, more product will be formed and hence catalysts are incredibly useful since, by definition, they are not consumed by the reaction - i.e. you get the catalyst back so it can continue to do its work.

Here's a good example of how enzymes catalyze reactions: https://pdb101.rcsb.org/learn/videos/how-enzymes-work

The last 1/3 of this old video from Shell describes how catalytic cracking, a crucial part of oil refining, works. It covers practical reactor considerations, including getting the products out so more are formed and 'poisoning' where a catalyst's efficiency is reduced by contamination and how that's dealt with in a continuous process. https://www.youtube.com/watch?v=hC1PKRmiEvs

We still don’t know exactly how catalysts work, because they operate at high temperature and pressure, so it is very hard to study.

That doesn't seem right. Cars have catalysts where the air flows through. Also 2 H2 + O2 -> 2 H2O (+ a characteristic bang :-)) at room temperature and pressure (initially) using a platinum catalyst is shown in school chemistry classes.

Just learned on Wikipedia (en/Platinum) that the 2007 Nobel price in Chemistry was awarded for explaining how that works. doi:10.1002/anie.200800480

Car's catalyst work at high temperatures, not at room temperature.

In fact, at room temperature they don't work at all, which is exactly the problem with catalysts, they don't work when you start your car.

They need to heat with the hot combustion gases to start working, and that takes a while.

This is one of the reasons that laboratory's measurements of particles and gases like nitrogen oxides do not apply to real emissions in cities, because most people in cities will use the cars, for example, diesels in Europe, for very short periods of time, then let the car cool down and use it again to go back less than 10 kilometers away.

There are many kinds of catalysts beyond materials surfaces. Organic chemists use metal complexes as catalysts in organic synthesis. This is especially important in asymmetric catalysis where you want to form high excesses of one isomer of a molecule, which can have drastically different effects in medicine for example. Catalysis also plays an important role in biology I believe.

This is completely wrong. Many catalysts work at room temperature and pressure and in many cases we understand very well how they work.

And our bodies are full of those. Enzymes are catalysts.