Yes, it’s equity not liability. But if you ISSUE stock, it’s on the liability side of the ledger. The balance sheet equation makes this clear: A=L+E.
That means it subtracts from assets.
And if you own stock, it’s obviously not an equity, it’s an asset— one with a corresponding entry on the company’s ledger, on the liability side, as equity. To make this clearer, if the company is dissolved, it gives it assets out to those holding its liabilities, first to the creditors (to discharge liabilities,) then the equity holders. The equity is what the companies “owes” to its owners.