Your thought experiment is assuming that $1T is permanently locked "in a vault", therefore it is not actually part of the monetary supply, since it can't be spent without violating your assumption.
Not quite, it's not permanently locked, I have just decided not to spend it. Ditto money people squirrel away in mattresses or vaults. It is an analogy for a change in behavior of market participants over time which must by necessity be included in any complete model of an economic and monetary system. Broadly speaking, "velocity."
This system remains at equilibrium because supply went up, and velocity went down leading to neutral price action.
I think what you're ignoring here is that as any individual gains access to more liquid wealth, they become increasingly more likely to spend some of it.
As your access to supply increases, your demand for more monetary units decreases. As your demand for monetary units falls below your demand for other goods and services you want in life, you spend some of it.
This is how markets function, right? This is why bubbles pop for example, eventually holders of an asset reach a price where they want to take some off the table.
That's the point though, inflation depends a great deal on the velocity of money, as much or even more so than the total amount printed.
Money in a vault has zero velocity, money being spent dozens of times a day has a very high velocity, most situations lie between, we need a meaningful way of discussing this that "monetary supply" does not capture.
There is a common idea that high monetary velocity (GDP divided by broad money supply) is needed for inflation. However, the data show that this is not the case.
This system remains at equilibrium because supply went up, and velocity went down leading to neutral price action.
It analogizes this graph: https://fred.stlouisfed.org/series/PSAVERT