Nope, I doubt it. It's much easier to sell shovels and still benefit whether the price goes up or down.

If price will reach 1,200$ in next three years I think the volume will be much lower

This will be the main mechanism positively correlating BTC price with Coinbase's stock price. The correlation will be weaker than that with MARA and RIOT though.

At the time a lot of gold was mined in California, the gold supply increased a lot as well. With Bitcoin the supply is algorithmically limited.

Well real world gold is also limited. The California mountains used to be rich with huge veins of gold and now while you can still find some in these places it is very rare compared to the 1800's.

Trading activity can still be high regardless of new supply, and that is what Coinbase is capitalizing on.

Gold price dictates how many shovels are being sold.

Similarly BTC prices dictates gross volumes.