‘Statistical significance is not clinical significance’ makes sense in the situation where you have stat sig result and rule out a notable effect (which probably rarely happens). But actually, it gets trotted out to try to salvage horribly imprecise results.
There is another situation where it gets used, which is a when a clinician wants to disagree with a statistician, and just needs something to say. It won’t actually relate to anything in those situations.
In most cases, I think use of that phrase tends to be a decent signal that the user does not really know what they are talking about.