AFAIK, nobody has ever managed to formalize any. Economists either imposed them by definition and let it float freely... Yet, the thing is very clearly highly constrained on practice. So the flow volume (MV) is somehow highly dependent on M, but not completely defined by it.

Excess capacity to supply doesn't mean there is excess supply. Supply is restrained due to lack of demand.

With excess supply capacity, Firms don't generally run at full output unless there are orders to fulfil. But that doesn't mean they can't then ramp up if the orders come in.

It's when capacity to supply is exhausted that we get price inflation.

"The price of commodities around the world is going up, by definition this cannot be due to a lack of competition - there must be something else at play."

If prices are going up there is a lack of capacity to supply, therefore there is insufficient supply which is why prices are going up - to eliminate demand.

At root the shortage of energy feeds into everything else.

There is no competition. No supplier gets a 'no deal' bid to their offer. They can sell everything they can make at the price they set.

That seems like it’s missing a variable to describe when increased supply is spent vs when it is saved.

If stock increases but is not channeled through flow, i.e. i take a loan at 2% to save in my bank’s savings offer of 5.25% then flow stays the same (i still spend on the same things each month) but money supply went up and inflation remained uninfluenced by my activities as supply slowly regresses to almost prior state while i pay off each month. Not quite prior stage because i get to save the extra from interest rate arbitrage.