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> but is there a paper dollar corresponding to every dollar I have in my bank account?

No.

> I always assumed that some of the currency issued by governments was exclusively digital.

They aren't even really issues by the government for the most part. While government policy shapes the framework in which money is created, much is created by private lending.

Most banks are required to keep 10% of the deposits

https://www.investopedia.com/terms/f/fractionalreservebankin...

Electronically, in an account at the Federal Reserve

They have to hold 10% of deposits overall, not in physical currency.

You don’t have dollars in your bank account, you have your banks promise to give you dollar if you ask.

No, most is digital, but there have been some interesting attempts

https://en.m.wikipedia.org/wiki/Trillion-dollar_coin

The accounting is tied to the Federal Reserve by mere bookkeeping for the bulk of it. If the banks are short on cash, they have the fed just print it for them.

This is what I imagined and would seem to prevent the vault-size problem.

Interesting.