"isn't it also being loaned out as well"

Hm? In the stock market, you pay a current stockholder for their share(s). The company sees no money from the transaction. It sounds like what you're thinking of is banking, which is something different.

I was mostly thinking about brokers. If I buy stock and hold it in my brokerage account, doesn't the brokerage use that money and stock to generate even more wealth? For example, they might loan my stock to somebody that wants to short that company.

incorrect. the company sees money from the transaction in several indirect ways. the existence of the market is what enabled the company to go public in the first place.

They also see money from the increased valuation of the stock they are still holding. This can be used to be borrowed against or sold.