You are sprouting things that are irrelevant to discussion.
And as shown above money supply in general means nothing if it can't reach spending phase. Gov can give every person younger than 30 100k for their pension plan - it's a huge amount of money printed that will not affect prices for the next 30+ years, because you can't actually retrive this money and spend them.
It actually just about spending money. Economic output blablabla is second-order factor that can be just tossed out as irrelevant.
Especially when we talk about inflation, where "economic output" is just a small factor in general equation "fair price" = "money available for spending" / "goods available" (and yes, economic output just increase "goods available" part, but it is not so important in general discussion about inflation)
Bottom is a common people that actually buy things.
It's important to understand who drive the actual demand part and it is not the top (goverment bodies). Top can stimulate, control etc, but demand itself is a bottom thing.
Why it's important? because demand can be reasonable, that is somewhat predictable and controllable and it's responsibility of the top to manage it, and unreasonable, driven by psychological factors ("consumer rush" etc). For example PS5 slim disk drive has almost 100% inflation now and it is unreasonable, hard to predict and control, because it driven purely by psychological factors - fear of shortages, fomo, trying to get ahead etc. It's not really normal. It create unreasonable high spike in demand that not covered by increased supply and prices skyrocket.