Thanks for elaborating, I think this distinction does actually make sense. I do however still think that the this definition of intrinsic value does not really matter for justifying a "real" price. The intrinsic value ultimately is still backed by transactions that are at some point themselves market set prices without intrinsic value. There isn't any natural law that would say fix the price of 2 oranges to 1 apple that could support any particular trade. You could also for example use this definition to talk about the intrinsic value of equity in a bitcoin only exchange (from trading fees), which would obviously become zero if bitcoin went to zero.
You're right that price is always defined by supply/demand and not directly by intrinsic value.
It's also true that intrinsic value can be different for different people, depending on how subjective it is. Gas may be worth up to $10/gallon for me, because without it I can't make any money. If I work from home, I may only be willing to pay $1/gallon for gas. Thus intrinsic value is usually a function rather than a static property, and inputs change over time. A consumer who is a billionaire may also be willing to pay a far higher amount for a good than somebody who's middle class. This could push market price higher, despite the core value of the good being unchanged. The value function is always there though, and it likely has millions or more parameters with different weightings.
So TLDR; price is a market determined value, intrinsic value provides justification for demand, which feeds into price.
A bubble is usually a result of price running far ahead of any justifiable intrinsic value. When price is far ahead of intrinsic value, it usually means it's being driven by "speculative value". Pokemon Cards, Fine Art, Wine, Beanie Babies. The actual use value of these is minimal, but people buy on the expectation that people in the future will value it even higher. You can make a lot of money via speculation on things like this, but there's also nothing supporting the price.
For an alternative example, if I buy a stock that yields a safe 10% dividend, then I can easily quantify the worth. I put $1m into it, and I get $100k a year forever. Can it fall 50% in value to a 20% yield? It's pretty much impossible, assuming the market believes the yield is safe. This is why fundamentals and intrinsic value matters a lot in investing
