Is there a standard definition? Does it have a unit? Is it even a number?

I’m going to take a stab. Without loss of generality I’ll define liquidity availability for buying (selling is analogous), as a unitless function \(L($,s)\) over transaction amount \($\) and time limit \(s\). Operationally, it means to take \($\) amount of a tradable asset, convert into number of shares \(N\) at the current price (assume it exists) and request to transact \($\) using all possible algorithms that complete in \(s\) seconds and find the one that got the most shares \(N^*\), then \(L($,s) = N^*/N\), a number between 0 and about 1 (for most cases). The larger it is, the more liquidity there is at the \(($,s)\) pair. \(L\) is monotonically decreasing in \($\) and monotonically increasing in \(s\).
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Treasury sells $40 billion in bills for Fed at 0.30%

The Treasury Department issued $40 billion in 35-day cash management bills Wednesday at a rate of 0.30%. Proceeds from the sale will immediately be transferred to the Federal Reserve to fund its operations to improve liquidity in money markets. The sale was needed to help the Fed expand its balance sheets, which has been shrinking as it lent out cash to banks and primary dealers to keep the financial system working.

Not nearly as bad as this scenario, where

… the accounting trick is simply for the Federal Reserve to “agree” to “buy” worthless assets like new government bonds that nobody else wants and for the government to turn right around to “fund” the Federal Reserve with the new money it got.

In fact, quite the opposite. I’m glad that people still want Treasury bills, even to the tune of zero (and perhaps soon to be negative) yield. I guess there is really no alternative. Where else is money to be kept … I would keep it where people/companies are most willing and able to produce valuable goods, but these are hard to identify clearly these days, so a proxy is as good as anything.

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