Don't know about that but the origin I'm aware of for "pulling yourself up by your bootstraps" are the tales of Baron Munchhausen, who is supposed to be a fantastical liar telling tall tales that are clearly ridiculous. Specifically I think he retells an adventure that involves him pulling himself out of quicksand (which btw also does not behave in reality as it does in fiction) by pulling on his own bootstraps.

So I guess the original use does kinda resemble "an incredible feat that strains belief" with the difference that it is supposed to be incredible because it's physically impossible to pull off. The current use for "making sensible spending decisions" seems to be the result of the phrase being overused to the point where the feats it describes become increasingly mundane.

I don't have experience with quicksand, but one can retrieve a stuck boot (that you're still standing in) from thick mud by pulling up on your bootstrap (or where it would be). You break the suction by lifting the heel, but the foot itself pulls out of the boot, so you have to free yourself by your bootstrap ... you just can lift yourself into the air that way!

The idea with quicksand was that you would keep sinking in it until you drown (imagine it as a bottomless pit). So pushing down on it would only get you stuck further. Pulling on your bootstraps would do nothing because by pulling on them you would need to push down elsewhere and thus still continue to sink.

In reality you can't drown in quicksand because it's more dense than the human body. To avoid getting stuck it's entirely sufficient to just move slowly to loosen it and break the suction as with mud. Pulling on your bootstraps is useful to free your boots but entirely unnecessary to simply free yourself. But this expression refers to escaping the fictional trope, not the real thing.