> Private banks increase money supply by lending. If 10 people deposit $1000 in a bank, it can loan $9000 to an 11th person

It's the other way around. When a bank loans someone $1,000, they create a $1,000 deposit (their liability) and a $1,000 asset (their loan). Loans create deposits.

The Treasury can mint coin. But that's basically negligible in modern economies.