Involving additional staff members in PhD supervision (beyond co-supervisors)

At least in my bailiwick, mathematics in the U.S., I've always been willing to answer questions if I could, without necessarily thinking about official obligations or channels or prohibitions.

Yes, in some cases, oddly, I was chastised for talking to "other peoples' students" down at the coffee machine, etc. Unclear to me the genuine motivations for such complaints.

But, indeed, my own picture of, for example, "a math dept", is that people profitably talk to each other, without formal rules or arrangements.

That's fairly common (at least in my field). In a CV, the involved staff member could specify their role in this PhD project as "assisting supervision", to distinguish it from a formal/official co-supervision role. Of course, such an involvement should be discussed with the formal supervisors first, since it might otherwise lead to tensions.