Paper money makes up only about 10% of the total money supply. The vast majority of USD is just represented by data in a ledger.

Which is an order of magnitude easier to come by, proving OP's point.

The system isn't that simple?

The US Government sells treasuries and bonds to raise dollars. These have to be approved by congress, which is why every so often you'll hear about government shutdowns, because, yes, if for whatever reason, the US Congress doesn't pass a debt ceiling lift, the US Treasury will not have enough money to run things anymore.

Then there's the Federal Reserve, which loans dollars to banks to create liquidity and velocity in the monetary system depending on certain conditions (Primarily inflation and unemployment I believe).

(Presumably there's a fair amount more to it than that as well).

The real fun begins when the fed starts buying treasuries.

What happens then? Don't they already do that?

Digits overflow would be a more appropriate concern

I think the OP is saying that you can have a situation where the short term demand for dollars outstrips the supply available at that given time (think in terms of hours or days). This could lead to a sharp but short increase in the value of the dollar, since there's only a limited, albeit extremely large, amount available on the market at any given time.

The bank needing the currency asks the central bank for the extra currency and it’s simply a number in a “database” somewhere. It can be done rather quickly.

it's not the bank, but the borrowers who need the currency.

So an increase in borrowing from various parties pushes the interest rate higher (the banks would want to charge as high an interest as possible, but no higher than what would make the client move to a different bank for the loan).

The central bank could potentially alleviate and increase borrowing without interest rate hikes by allowing the banks themselves to obtain funds from CB at a lower interest (than another bank), and the competition between banks would push the interest rate back down.

The entire value of the currency is based on supply and demand, whether the gp is correct in their prediction, increased demand relative to supply is the defining mechanism of how a currency's value would increase.

I take the post as the US dollar becoming more scarce but not running out.

If OP is right I don’t see the federal reserve acting to bail out China.

They might happen to do QE for another reason but not to help out other countries with their problems.

As the bank of the world's reserve currency the Fed is always implicitly running a world bank. The transmission mechanism is for foreign currency to depreciate against USD which causes US domestic financial conditions to tighten, and the Fed would then have to loosen.