Did the Ba'ku really need to say they calimed the planet?
Yes, it certainly would have helped their position. Not that I think i would have made much difference in the end.
It's not clear if the Baku even thought of the planet as theirs.
They settled on it prior to the founding of the Federation.
Which wasn't the case. The Baku might not have possessed a warp driven ship at the time of the movie. But they were a warp tech culture. How else could the Baku have forced the Sona off the planet? How else could they have migrated there from their "birth world?"
It is much more like the episode Ensigns of Command. Where a group of people settled on someone else's planet, and needed to be removed for their own safety.
In INS they want to move a group of people to get at something ...
Once again, it wasn't necessary to remove the Baku to harvest the rings. The Baku were to be remove so the harvesting process would not harm them. But their removal wasn't essential.
it was a humanitarian move.
It seems clear from the movie that the council wasn't told the full story ...
How so? What didn't the Council know that was relevant?
The Council already knew it was a Federation planet.
The Council already knew the Sona have the tech to preform the harvest.
The Council already knew the rings will provide health benefits to many billions.
The Council already knew a warp capable group of migrants were on the world.
The relationship between the Baku and the Sona is a side issue. The health benefits are still there, the planet is still a Federation planet.