The "Kyu" story was more for a morale booster because BoA's PR division was kind of caving in on itself from how quality had nose dived and they had been in a tailspin since about roughly Super Megaforce on not knowing wtf they were doing. They rather oversold that Kyu story more than was true. It's a whole thing of bad choices, and other factors that eventually lined up to why Hasbro had to step up to the plate to take over. BoA was killing the brand in bad choices and poor execution with how it was entirely mismanaged in chunks, whereas other areas were trying their best to keep them afloat. The sad thing being that the movie toys were held in check by those development arms trying to keep it afloat, and those were the best sellers BoA has had in a bit. Those same areas are what tried to reinvigorate life into the brand in other ways too, but it was already a sinking ship at that point. Which was really sad to see because they'd done such amazing work previously for other shows in the past. BoA's PR team tried to blame anything and everything they could when the consensus had always been it was poor design decisions, poor implementation, and low quality of content that was killing the brand, not the reasons they tried to blame.

Anyway, though to answer your question. Hasbro owns it all when it comes to media material as part of the purchase, only toy originals that were never in any medium are likely not included. So that includes all material for Kyu if it gets adapted, and is likely next anyway. But random toy originals like the Jungle Fury bike megazord or car megazord are a no. Only things that are actively in the shows or comics are held in the rights.

Might be some loopholes to that like the Jungle Fury Super form masters if they weren't in show, since those are show aesthetic. But generally speaking, toy originals that aren't in show aren't considered part of the overall rights.

It works much the same as comic character rights from what I've been told. If it premieres in a comic or the show, it becomes part of the media rights itself, unless it premieres in something not Power Rangers related before that.