0 Ohms only exists on paper or by assumptions when higher loads can neglect the effects of current limiting. We call this real resistance or effective series resistance ESR and it exists everywhere in caps, batteries and even the AC grid and EE lab supplies.
The error is due to the limited feedback gain to correct the error to make the loop stable. The loss is initially defined by a series pass transistor Ron then reduced by its feedback loop gain by sensing the error voltage.
Normally I define ESR as a percent of rated max load which is the inverse of load regulation drop error. On the AC grid, a transformer impedance is rated the same as Zpu or per unit of rated load impedance.
So if a car battery can crank 1000 Amps while dropping to the test voltage from 12.5V to 7.5V or a 5V drop, we can say its ESR is about 5V/1000A = 5mΩ
So we expect the load resistance of that battery test level to be 7.5V/1000A = 7.5mΩ for the same result as the CCA crank spec. Usually, the start is much higher than 20mΩ in warm weather with less friction so the voltage drop is less.
You lab supply may have a current limiter or not, but it's ESR or Zout or source impedance at DC is defined by that incremental drop in voltage with a drop in short circuit current. or ESR=ΔV/ΔI which is some % of the min load R at max power with Vo/Imax=Rmin.
A good design is 1~2%. A great design is better, and not so good worse.
Here is another similar query.
Its good to know the limits of our test equipment, so keep exploring. Of course, there is reactive storage energy in the output cap, so peak power currents and durations will be higher. But don't overdo it with pulsed inductive loads putting energy back into unknown protected sources.
I always am aware of the ESR of all components and it varies widely and with frequency as well. It can be used for a transistor or diode or LED saturation and is inversely related to the Power capacity of the part.
Often it has different names like ESR for dielectrics and Rs for conductors, and DCR for inductors or RdsOn for FETs and Rce for BJT's.
Yet no one can make true 0Ω but get pretty close with cryogenic superconductors for MRI's.