You still haven't answered how much resistance a short must have. Tick, tick, tick...
A short in theory means 0 resistance. That's 0.00000 with infinite number of zeros after the decimal point.
It does not matter if there is 1 picoohm, that's not a short when we consider pure theory. Sure, in practice we will most likely never see that nor use it, but that's theory for ya
Note that when we read about circuit analysis we might see "To create the supernode we short point A and point B together, then do the analysis."
It does not say, "To create the supernode place a 1 picoohm resistor across point A and point B, then do the analysis".
How is this different? It's different in a variety of ways, but of course it's relative just like with the RC low pass filter question.
Let's say we have a voltage divider with R1 and R2 and input voltage 10 volts. The formula would be:
Vout=Vin*R2/(R1+R2)
Now say we had a gap between the battery (Vin) and R1. That would mean no current flow yet. Next we would say "Short out the gap and do the analysis". When we do that, we get the formula:
Vout=Vin*R2/(R1+R2)
as before.
What happens if we use some small resistor value (like a 1picoohm resistor) instead of what we just called a 'short'?
Here's what we get:
Vout=Vin*R2/(R1+R2+R3)
We had to introduce R3 because we don't yet know if it's 1 picohom or 2 picoohms etc.
Of course this is pure theory and probably not practical except in a lab where it matters.
So sometimes we either have a resistor or we don't but this is not the only case where this may come up. If you recall, there is such a thing as a "zero ohm resistor" in an SMD package, and also I think in a 1/4 watt through hole component (maybe others). In that case it's a very practical thing.
So again we run into the casual conversation vs the pure theoretical conversation. In some cases we call it a short and mean a direct short with no exceptions, and other times it does not matter if we use a 1mOhm resistor even.
If you don't feel comfortable with this that's perfectly fine, but sometimes when someone says "a short" they mean an actual short with no resistance whatsoever, and no inductance, no capacitance, no external fields, etc.
If we turn to pure physics on the other hand, we may be able to prove that there is no such thing as a short. That would be a practical result if we could, and yet circuit theory would still go on to say that a short is a perfect zero ohms. The difference here is physics theory vs circuit theory. They both have associated assumptions. If someone says a short is a perfect zero Ohms, then they are talking within the context of circuit theory in its purest form. There is no reason to reject it within that theoretical scope.