yeah, I've long wanted to do a deep dive into all of these.

My short, intuitive answer is that monetary inflation does show up in price inflation. That is, aggregate prices (#820834) don't increase unless there's money expansion involved. (The reverse isn't always the case: money can expand without prices doing anything, either because 1. they show up in assets and/or go overseas, or 2. they stay fixed in the banking system and thus never hit the real economy where they could bid up prices/wages)