tldr: the big banks held a bunch of MBS (Mortgage-Backed Securities) that were worth literally $0. The Fed came in and said: "every security that you own, if it is not profitable, you can sell it to us at face value. We can print as much money as we want". So the banks were able to easily get rid of anything that wasn't profitable for free (with no losses), that is why banks instantly returned to profitability. The Fed still owns all of this, $2T of the 2008 bailouts are still on their books. If they undid even ~10% of that continuous 2008 bailout and unloaded it on the market, the entire market would crash.
A lot of what you're saying is misleading (intentionally?) or wrong. Most of those MBS are post-crisis, and all of them have a full credit guarantee from Fannie, Freddie, or Ginnie. There aren't any defaulted loans in those MBS. A lot of what the Fed is holding is worth less because interest rates have gone up, though