Currently I don't think there exist any relationship between bitcoin and the stock market. All the changes that we see on the crypto market is many due to the activities of powerful crypto enthusiasts. Usually changes on the crypto market are mainly due to manipulations.
It has changed for the worse for us. Back in the day when there was a crisis somewhere in the world people moved their money to coins so they would be undamaged from the crisis. When greece had a economical crisis people bought bitcoin as much as possible so when the government wanted to put a limit on stuff they wouldn't be affected.
There was people from cyprus who had lost millions of dollars because government was badly managed and they needed money to pay the debt and did some insane stuff so all of them moved their assets to crypto. Nowadays when there is a market crash somewhere people cash out their crypto first, stock markets became once again a popular option for investors instead of moving their money to crypto. It became one of the first things to cash out.