There are smaller tests for liquidity, but the specific major stress test that SVB lobbied themselves out of is the DFAST (the Dodd Frank Act Stress Test) and it does not test liquidity. It takes the scenario of an adverse economic situation and comes up with a bunch of hypothetical numbers you might see for major economic variables - “the unemployment rate will be this, the default rate will be that, etc,” - and then banks have to run their books according to those hypothetical numbers and report back what their capital would look like in that situation. If it looks bad, they have to take action to make their capital more secure. Nowhere does it simulate a situation where depositors leave en masse.
There are liquidity tests and SVB was probably failing them (which is probably why the FDIC was paying close attention to them), but that specific test you’ve heard about is not related.