You can say that whether it's signaling is determined by the motivations of the person taking the course, or the motivations of the people offering the course, or the motivations of employers hiring graduates of the course. And you can define motivation as the conscious reasons people have in their minds, or as the answer to the question of whether the person would still have taken the course if it was otherwise identical but provided no signaling benefit. And there can be multiple motivations, so you can say that something is signaling if signaling is one of the motivations, or that it's signaling only if signaling is the only motivation.

If you make the right selections from the previous, you can argue for almost anything that it's not signaling, or that it is for that matter.

if someone wants to demonstrate some innate or pre-existing quality (such as mathematical ability), they participate in a relevant contest and this is signalling.

If I wanted to defend competitions from accusations of signaling like you defended education, I could easily come up with lots of arguments. Like people doing them to challenge themselves, experience teamwork, test their limits and meet like-minded people. And the fact that lots of people that participate in competitions even though they know they don't have a serious chance of coming on top, etc.

OSHA rules would still require that the crane operator passes the crane related training.

(Sure, but I meant that only truck drivers would be accepted into the crane operator training in the first place, because they would be more likely to pass it and perform well afterward.)