Correct

Think of options as side bets.   Traders use options because of leverage.   So they are not buying or selling bitcoin they are trading contracts on the side betting if bitcoin goes up or down by a certain date.

But options market makers are mostly writing the options.    Its really risky for them to do this so in order to hedge these bets they buy or sell the underlying.   Its called delta hedging.   Delta us how much the option mives w the stock.  The stock is one delta.   The more "in the money" the higher the delta.   Market makers don't care about direction.   They make money on premium and the premium is priced using volatility

When a product has options it gets traded a lot.   But its the same shares being passed back and forth by the same group of market makers.   This is why liquidity increase.   If you need to buy or sell the market maker takes your order.   You don't need to wait for a buyer or seller on other side.