I don’t disagree with your interpretation of “you’re welcome”. At the end of the day, it is still a phrase which sort of weakens a “thanks”, out of politeness.
I’m saying that there’s a difference between “you deserved that thing already” and “there was nothing I did, which anyone would need to be deservent of”.

And “de nada” is actually a bad example here. Yes, the dictionary will tell you that it’s a valid translation for “you’re welcome”, but the actual words translate verbatim to “of nothing”, as in “you’re thanking me for nothing”. So, “de nada” is very much like “no problem” in Spanish.