I'd argue BTC is backed by resources, primarily the highly valuable resources of time and energy, which are both finite, unlike paper money which we can pretty much print indefinitely out something (even fast producing algae). On the other hand, you can't print more energy as that would break the first law of thermodynamics, and it is not currently possible to create more time, though using Einstein's theory of relativity, theoretically you could have someone mining BTC in a time vacuum running circles around the rest of the universe, but they would be moving at speeds faster than currently possible to achieve, and one mus then wonder, would the BTC actually have value left after the costs of that space trip?
So, realistically, BTC has value because it is supported by non-renewable resources.