The death star has no intrinsic economic value. It produces nothing, so it's destruction shouldn't really change anything. It could only ever be back by either taxation or the printing of money. This doesn't change whether it exists or not.

The destruction of the death star may reduce the burden since it would no longer incur operational costs. On the other hand, it did establish the operators as a tax authority.

I would expect lending banks to be covered by printed money followed by corresponding inflation. On the other hand, if the lenders are isolated among relatively few planets/systems, they could be overtaken by the government and those systems would bear the brunt of the losses.

The most likely outcome wouldn't be galactic recession, but return to chaos and war as the grievances between systems would now be unchecked.