The colloquial definition is "Useless but impressive and flatters my vanity".

Useless to whom?

Newton was respected for coming up with useful theories and natural science, not just pure philosophy or non-applied math. You could maybe argue that his work was rarely useful to him personally, so he only did it as "signalling" to get respect from others to whom it was useful. But under that theory, any division of labor where people are paid money for their work which is only useful to others would be called "signalling".

The probabilistic definition is "Observable thing X signals quality A means P(A|X) > P(A)".

That's true: that Newton came up with good theories in the past is evidence he'll come up with more good theories in the future. It signals his quality as a scientist.

But this is a good thing (as opposed to the usual negative implied connotations of "mere signalling"). And the reason it's a good thing is that his scientific work was actually useful, so it's a good thing others could identify this and reward him to make him do more useful work.

The economic definition is [...]

That's just saying "people will choose to signal if benefits exceed costs". It's true, but it doesn't explain to me the original statement:

With the worst privileged questions I frequently find that the answer is "nothing," sometimes with the follow-up answer "signaling?"

Which says "signalling' in this instance is something that motivates people in the absence of things being useful in their own right.