Credit has been one of the engines of capitalist growth. In fact, real capitalism did not take off until the Italians invented banking.
And, no, central banks don’t become socialist just because you call them that.
Credit that grows to the point of debt slavery, where people can’t pay anymore, is slavery. The government can’t pay, the banks are insolvent, and the average citizen is tapped out. Credit bubbles pop, and kill the fiat currency.
That is not capitalism.