Is there actually such a thing as a "slow thinker"? I find it hard to believe that slow thinking skills doesn't heavily correlate with fast thinking skills, is there any evidence of this?

Note you have to rule out stress, since stress is not related to this. Performing badly under pressure just means you are not stress resistant, it doesn't mean you are a slow thinker, you can still think quickly when you are calm.

So to me it seems like labeling yourself as a "slow thinker" is just putting unnecessary limits on yourself. "I am not good at that, I am a slow thinker" is defeatist.

This rings of fast-thinker ableism.

I think I'm a slow thinker. And that's because I have ADHD and a number of learning disabilities including dyslexia and dyscalculia, and also short term memory problems. It takes me twice as long to do things as normal people. I'm smart, but if the game is "do this thing quickly and accurately" then my results will make me seem very dumb. I did manage to get a Ph.D. but only because it's the kind of thing that doesn't require you to be fast and accurate, but slow and deliberate. I can do that very well. But then people see the Ph.D. and think that means I'm a fast thinker, and they are often very disappointed I am not.

So you're right, I do self limit by labeling myself as a slow thinker, but I think it's for the best because otherwise people overestimate me and end up disappointed.