Correct me if I'm wrong though: equity is issued in net positive supply. And while the company has equity on the book as a liability, that liability does not go up when the stock price goes up, right.

Thus, when stock price doubles, it is wealth creation for the shareholders (and if they'd sell to someone else, it would be realised).

Edit to add: unlike derivatives (like call options), which are in net zero supply, thus their payouts are always zero-sum.