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What do interest rates offered by the banks have to do with liquidity in the bond market?

The Fed speculates that the reason for the lack of liquidity is due to uncertainty about the economic outlook and uncertainty about the interest rates. The evidence they point to is that liquidity (defined by the bid/ask spread and the amount of available bonds at the best price) is lower for short-term bonds compared to long-term bonds. Short-term bonds are more affected by interest rate changes, so market participants are much more cautious about transacting in a large number of bonds at once. Rather, they split large purchases into many small purchases to ensure they're not losing money due to sudden changes in the price.