I think if Harry didn't consult the queen she may not have been happy with it.. not because she doesn't want Eugenie to have it but because she may want to keep it free in case H does come back.. or she was annoyed at not being consulted. But I find it hard to believe that she'd say that E and Jack had to leave.. or didn't like the idea of them living close to her...
So it is odd. I suppose if they did move in and now have moved out, the most likely explanation is that they found they didn't like it for some reason or it wasn't convenient for them and now they are going to settle somewhere else..
In the event Harry (or Harry and Meghan) does come back then they'll find somewhere for him/them. It's not going to be dependent on Frogmore, especially as the couple may not have liked it very much in the first place. So she may well not have agreed with how the arrangement happened but I really don't see her saying Eugenie and Jack have to leave if they had already moved in, especially as she's due in the near future and it makes sense to be near her parents and in a bigger house than Ivy/Nott Cott.
If they did move in and are now moving out then it must have been deemed unsuitable in some way. Or perhaps there's an issue with the building like plumbing?
They must have seen it before deciding on this arrangement so suddenly deciding they don't like it would be strange. And they're used to living outside London.
I'm sure there will be more on this ongoing Saga of Frogmore later.