It's less about being a power. The British Empire was "A Power". The US is "A Power". Russia has been "A Power" and wants people to think it still is. China is "A Power".
Unless you use it to the benefit of the people, it's just posturing.
placed by the government in the custody of the Picard family
Is that something included in Picard? Cause it seems like a significant departure from the rest of the idea of the series. The government of the federation doesn't allow people to do things at it's whims, it facilitates people's freedom to do what they want to better themselves.
His family has had vineyards for generations. Why wouldn't they be allowed to? Space isnt exactly a luxury since they have dozens of worlds you can move to and have your own.
Keep in mind the "Gay Space Communism" isnt the soviet dictatorship kind where everyone is allotted their resources and you're only allowed to do what the state says. Its a post-scarcity world where people can follow passions and personal drive just because they want to. (As long as you learn calculus) Something explicitly stated multiple times in the series.
They have the luxury of the philosophy of improving one's self and the environment for others.
Assisted a terrorist in almost blowing up the wormhole (against her wishes, mind).
Went to rescue a ship of Bajoran prisoners only to bring back Gul Dukat's daughter.
Those are two more I can think of.