I define "intelligence" as "having a strong ability to hit narrow targets in a large search space"

If you make a too general definition, you may hit the No Free Lunch Theorem. For every universe where X is an intelligent strategy, we can design a Troll-X universe where using that strategy always results in a disaster. (An angry god measures your IQ, and hits you with a lightning bolt if it exceeds 150.) So the question is, what is intelligence in our universe.

Also, we are humans. As long as a test measures the ability of a human to hit narrow targets in general, we don't (yet) have to worry about the test being unfit for some machines or aliens.

Also, is there a one "official" IQ test?

No, there are multiple IQ tests that have been calibrated on large population samples, and they correlate to each other.

or does any random internet thing that calls itself an "iq test" work?

Obviously not.

which ones are real?

No online IQ test is real. How would you calibrate such thing?

Among the actual IQ tests, Raven's Progressive Matrices are a solid test. There are also others, but I don't remember which ones.

if they are not good measures of intelligence by this definition, is there a definition of intelligence which they are good at measuring?

They are good at measuring "the thing that people you would intuitively call 'intelligent' have in common".

Like, literally, this is how psychometrics works. You choose a concept you are interested in, for example "intelligence" or "niceness" or "whatever". At first, you have no idea how to measure anything like that. But you can point at a few people who are obviously an example of that, and a few who are obviously not. So that's a beginning. We need to find a test where the former will score higher than the latter.

So the next step is that you brainstorm dozens of questions that seem related to the thing you want to measure. Then you give those question to thousands of people. You observe two things: (A) which people score high and which people score low, and (B) which questions correlate with each other; the formal way to do this is called factor analysis.

Then you think about the results. Like, maybe if the analysis shows that there are two or three factors, you choose the questions most correlated with each factor, and try to figure out what the questions correlated with the same factor have in common, and how they differ from the questions correlated with another factor. You find out that you have actually tried to measure two or three things, because you were confused about them, but now you can see that they are not the same thing.I

If you do this with the naive concept of "intelligence", you will find out that there is one big factor that correlates with your concept of intelligence, and a few smaller ones that are something else (for example fluency in English). So you take the questions that correlate with the big factor, and call the resulting score "IQ".

This is how it was traditionally done. If you believe that this does not sufficiently measure the "quality of hitting a narrow target", you may be right, and in principle you could follow a similar process to design a better test for that. You might find out (in the part where you do the factor analysis) that the thing you were trying to measure was actually a combination of multiple things, such as intelligence and conscientiousness. (Because there is a difference between "target-hitting" in abstract, and "target-hitting, as it is actually implemented in humans".)

My understanding is that IQ tests measure some dimensions of intelligence, but not others. That matches my experience.

Back when I was a kid I was administered an IQ test. I scored in the upper percentile, I’ve always been pretty good at reasoning, pattern recognition, and creativity. Those were qualities that the test I took measured, but I struggled (at least relatively speaking) with social, situational, and spatial awareness.

I think determination would be another trait wasn’t being tested for, but that’s important for hitting targets in a large search space. It’s quite likely that things have changed. It’s been 40 years now.