It absolutely does impact the national debt. The FFR is the range on inter-bank lending which the FED themselves state attempts to influence other interest rates. Also, the FFR is really just a target range; they still have to adjust interest on reserve balances to bring the actual rates down and you'll see they've done this: https://fred.stlouisfed.org/series/IORB

When a bank gets less return on excess reserves, it will want to make more loans. For regulatory reasons they have to hold some treasury bonds as collateral which again puts upward pressure on treasury prices. Rising bond prices pushes down treasury bond yields. Low yields on treasury bonds makes it easier for the government to borrow and rack up even more debt.

Generally, more liquidity to bid up assets, including treasury bonds (which are still attractive while yields are relatively high), will push down yields everywhere.