Put in practical terms, does a detailed knowledge of exactly how the slime mould works help in constructing an AGI? Does it help in constructing more limited sorts of AI? Does it illuminate the investigation of other natural systems that fall within the concept of "intelligence"?

I am not seeing a reason to answer "yes" to any of these questions.

Yes, to all of those questions. I don't think we currently have the AI technology needed to produce something with the intelligence of a slime mold. (Yes, we might be able to, if we gave it magical sensors and effectors, so that it just had to say "go this way" or "go that way". Remember that the slime mold has to do all this by directing an extremely complex sequence of modifications to its cytoskeleton.) Therefore, having a detailed knowledge of how it did this, and the ability to replicate it, would advance AI.