ProceduralDataflow | library uses the custom awaiter feature | Functional Programming library

First, short answers to your concrete questions.

Does it throw if CompleteAdding was called on any collection? or both collections?

Both (all) - but only if there are no available elements in any collection.

What if CompleteAdding was called and the collection still has some items, does it throw?

No. If there is available element in the collection, it will be removed from the collection and returned to the caller.

Conclusion

Apparently the documentation is unclear. The part

or CompleteAdding() has been called on the collection

should have been formulated differently - something like

or there is no available element in any of the collections and CompleteAdding() has been called on all the collections

Rationale

Well, I know relying on the implementation is not a good practice, but when the documentation is unclear, the implementation is the only reliable and official source I can think of. So taking the reference source, both TakeFromAny and TryTakeFromAny call a private method TryTakeFromAnyCore. It starts with the following: