If I scratch my nose, that action has no truth value. No color either.

The proposition "I scratched my nose" does have a truth value.

Bayesian epistemology maintains that probability is degree of belief. Assertions of probabilities are therefore assertions of degrees of belief, which are psychological claims and therefore obviously have or can have truth-value. Of course, Bayesians can be more nuanced and take some probability claims to be about degrees of belief in the minds of some idealized reasoner; but "the degree of belief of an idealized reasoner would be X given such-and-such" is still truth-evaluable.

See the distinction. Don't hand wave it with "it's all the same", "that's just semantics", etc. You started saying that this is more of a question. I've tried to clarify the answer to you.

The question was primarily about the role of probability in Pearl's account of causality, not the basic meaning of probability in Bayesian epistemology.