sorry if this came across as directed at you somehow. you seemed to have a more detailed understanding of the moving parts, so I figured I could throw a super simplified version of my understanding at you and see if it is a valid simplification or an invalid one. I'll interpret your answer as "invalid" for now. :)

No, it's not from thin air. Bridge financing is from cash on a bank's balance sheet (or as mentioned above, sometimes non-bank entities). Banks usually participate in bridge financing (some fees, loan on balance sheet typically on a short-term basis) because they want to also be part of syndicate financing (more fees, previous loan syndicated out to investors).

Banks infrequently get "hung" with loans and these usually are just bad deals that somehow got through. There are more hung loans now on deals that might have been okay under normal economic circumstances but are not feasible right now.