This is a fun question to me, because I don't believe there's one right or wrong answer.
In my parents' home, we were expected to work and never paid for it because it was part of . The work was ordinary household chores (just lots of them, because my mom is a neat freak) and outdoor chores of the sort a neatly maintained, landscaped suburban house needs. It was also help with woodworking or craft projects, construction (of sheds, additions to the house, etc.), babysitting (though only in my case, as the eldest) and cooking.
We were also expected to go to my mom's workplace a few times a year and help her with simple sorting, organizing, or decorating of her classroom (mainly because she didn't have a babysitter). A few times, my father made us help with his construction business, when he had one, but we weren't of much help because he wasn't a good teacher. When they had yard sales and such, we were right there helping with sales and counting change.
IF my dad had expected us to work full time at his construction business, we would have expected pay. He didn't do a very good job of paying his actual laborers (including some of our friends, but that's a legal story for another forum), so perhaps that would've been misguided.
But every family is different. My childhood best friend was expected to help with the family's eBay auctions for free, but was paid an allowance for her chores, which she rarely remembered to do (and thus constantly struggled with her mom over). Other friends were paid an allowance AND never expected to lift a finger for any household work outside their own bedrooms (and some even had maids for that work!).
Nobody did it wrong, per se, but I would advocate for giving children some responsibilities beyond their own welfare, paid or not.