Good question Mark. As you mentioned, it is a unit of capacitor's internal resistance. Ideal capacitor would have no (zero) internal series resistance. Tis value is taken ito consideration in AC circuits or in high frequency switching power supply filtering applications.
https://www.meanwelldirect.co.uk/glossary/what-is-equivalent-series-resistance-esr/But we simply use these caps as a temporary storage of DC energy (like a long -life rechargeable battery). No need to use the expensive caps with low ESR values. That is why nobody mentions it. Go ahead and get the less expensive caps - just make sure to have that voltage cushion you mentioned. It is better than the alternative (explosive fiery capacitor failure). I also recommend a burn-in of the new caps before installing them in your model. Attach them to a voltage source that is about 80-90% of their rated voltage for some time (like an hour). If there is a weak cap in the bunch, it will self-destruct before being installed in your model.
Don't forget to discharge them after the burn-in, so you don't get surprised by the residual voltage when you are installing them in your circuit. Discharging can be done with a resistor held across the cap's terminals for few seconds. Any value from a 100-1000 ohms will work. Or just short them terminals with some metal objects, but the you'll see some small spark (depending on the capacitance). Still, that is safe to do too (for the cap) .
