The volatility of Bitcoin has led to the shift in engagement because the price of Bitcoin can sometimes determine engagement. Like the economic variables; demand and supply. An increase or decrease in price, can lead to n increase or decrease in demand, conversely an increase or decrease in price can also lead to an increase or decrease in supply. From the aformentioned, one can say, the demand and supply can influence the price of Bitcoin.
It's simply the law of supply and demand is applied to Bitcoin's price.
Can more adoption and engagement influence the price of Bitcoin as st a particular date?
Yes. That makes the demand higher and so, makes the supply lesser in the circulation. Which means potential pricing could increase in the long run. And that's why we aspire that there will be more adoption to come because not just about people accepting Bitcoin and investing on it. But also, to make its price higher than it has been.