slows down may be the wrong way to think about it. Myelination is a very real thing though. By 24 the majority of the brain is grey matter, as opposed to pink matter. Grey matter is super fast at signal speed due to myelin sheaths around highly used neurons. The amount of pink matter continues to shrink as you get older. This seems to have measurable effects with knowledge, the main one being whatever you learned when you were younger is much easier to access and riff on when you’re older. It is believed that this contributes to it being more difficult to learn “new” things, particularly if they are unrelated to your current knowledge as you get older. (There is some evidence however that learning “new” related topics is even easier as people age)
So if someone says their brain is slower, they may be talking about how much harder it seems to be at learning new topics. I’d bet dollars to donuts they’re as fast a thinker on things they’ve been doing for 30 years as ever.