The stock markets and bitcoin go most of the times in the same way because the investors don´t care about the volatility and all of that fights about cryptocurrencies. When the investors see good news and want to buy, to make some money, the prices rise in both markets (it´s how economics work).
I thinks we can expect behaviors like that in the future too.
Probably with more impact in the crypto markets than in the stock markets.
I have a little conspiracy theory in my head:
crypto world + Bitcoin gives massive volatility, and price fluctuations on almost daily basis. This is excellent for traders. Also the fees are way way smaller than traditional stocks.
Traditional stock brokers, traders are leaving to crypto trading, for the reasons I mentioned in 1st point, but also they are leaving the companies, so there are gaps appearing. That's why in the future 3-6 months, we might see bigger and bigger stocks' price fluctuations, in traditional stocks. Maybe even trading fees reductions all over industry (Robinhood 0 fee, brings a massive change). So traditional banks JP Morgan, etc will try to "get back" those traders who left to trade crypto... In other words they will try to stay competitive.
It is only my opinion.