I'm confused about fiat money creation and debt in the US. My mental model is that the Fed lends money into existence (either to banks or to the treasury), which creates a loan (that eventually has to be paid back with interest, though I think they can choose not to collect on loans to the treasury?) (I'm also not sure where the money the Fed uses to pay interest on bank reserves comes from, but since it used to not do that I'll ignore it and pretend I'm asking about the time before that existed). The fractional reserve banking system then creates a convergent geometric series of additional money creation through repeated lending and saving, and that's basically M2. (I'm ignoring the fact that the reserve requirement is currently zero, I don't think it affects my question anyway).
It seems like that means that for every dollar that exists, there is an equivalent dollar owed in debt to someone. And conversely, when debt gets paid down, the monetary base decreases. This suggests that it is not possible, economy-wide, for private sector net savings to increase unless the government debt increases, and that whenever government debt goes down, private savings must decrease. I feel like I'm missing something central, because otherwise this would be public policy 101 level stuff that the Left especially would be very vocal about, but I can't figure out what.