“When a player claims the battlefield, if the do not control it, they take control of it and may use its “claim” ability”

Question: if you already control the battlefield and then claim it, can you use the “claim ability?

“That player chooses one of the 3 face up set aside battlefields, flips it over and may use its “claim” ability OR power action”

Question: so if you are the first player to claim you take control of the battlefield, can use the claim action on that battlefield AND you use the claim action on one of the three set aside battlefields?

Good question. Here's the way I would interpret it:

"The second and third players to claim the battlefield do not take control of it and do not use its “Claim” ability." I can infer from this that FFG probably intended the first person to claim the battlefield would use its claim ability, even if they already control it. As a result, the following sentence is two clauses, separated by a "|": "When a player claims the battlefield, if they do not control it, they take control of it | and may use its “Claim” ability." If they don't control it, they take control of it. Then they may use its claim ability. On top of it, they get to choose one of the three face-up set-aside battlefields and use it.

So, in short, the person who claims the battlefield first takes control of the battlefield and gets to use two total claim abilities: the one on the battlefield in play, and one on one of the three set-aside face-up battlefields. The second and third players to claim the battlefield do not take control of it, but they may use the claim ability on one of the remaining set-aside face-up battlefields.

Hope this helps!

This is how I have played it and how I have now interpreted it too. But the wording is a bit unclear. Thanks for responding!!