> every formalized definition I could findHave you ever looked at an actual textbook?
Even what you quoted does not define "demand" as price. It says "an increase in the price of a good or service will decrease demand"--which implies that "demand" means quantity demanded (at a given price). Which is how I defined it.
> an increase in price does not change the demand at all
I said demand (more precisely, the demand curve) is quantity demanded as a function of price. I certainly did not claim that quantity demanded does not change if price increases.
> Does your definition of demand always require that the buyer be so formal in their investigation?
No, it just requires a market. "Just saying" something does not constitute a market, but making an offer to buy something at a given price does.
> by your early definition of shortage meaning demand exceeding supply, means that virtually everything is in shortage
No, it doesn't. Let me restate my definition of shortage to make the definitions I have been using explicit: it means that quantity demanded exceeds quantity supplied at the current price. That is certainly not true of "virtually everything".
> I'm not sure where you got that idea
From what you said. You said: "Every time the price goes up, there will be buyers dropping out of the market not willing to pay the new high." Why does the price go up? If buyers aren't the ones setting the price (which is obvious since not all of them are willing to pay it), it must be sellers, i.e., programmers. So for your statement to make sense at all, there must be programmers available at the higher prices.
> We have acknowledged right from the beginning that price can stop rising.
I'm not sure who this "we" is that you refer to. You have claimed that "the price is rising", and that this will continue until there is only one programmer in the world who is working. That doesn't sound like acknowledging that the price can stop rising.