Is the Hajj considered valid, or is a Fidyah/Qada’ required for not staying overnight in Mina itself, given that the camp was located in Muzdalifah (its very beginning and Mina’s very end) and we spent the nights of Tashreeq there, and we were informed of its permissibility due to a fatwa that considers the camp to be in Mina if the rows are continuous?

What the camp organizers mentioned about the validity of your stay in Muzdalifah due to the lack of space in Mina is correct. If a pilgrim is unable to stay overnight in Mina after having made every effort to do so and being incapable of it, then nothing is incumbent upon him, and his Hajj is valid, because Allah Almighty says: {So fear Allah as much as you are able}, and His saying: {Allah does not burden a soul beyond its scope}.