They're moving it from one bank to another in most cases. In the cases where its being spent down (i.e. a lot of the startups that are burning VC cash on payroll, OPEX/CAPEX, etc.) that money was going into the economy either way, regardless of which bank it sat at.

What is happening though is a bunch of banks are getting defacto taxed to cover SVB and Signature's shortfalls on asset sales just to make sure those depositors can move banks, and that money that gets taxed will be replenishing the empty FDIC piggy bank for insurance. For the banks not affected by SVB, they're recapitalized with the funds they've borrowed, and then pay it back with minor interest to Treasury which gets to use it against the US budget anyways.