The dielectic is the oxide layer. They etch the aluminium foil to get a bigger surface and increase capacitance. So a thinner layer should give a lower capacitance.
But the peak and many multimeters use DC to measure bigger capacitance and a not formed cap eith a to thin layer often leaks to much current so appearant capacitance is high while true capacitance could be low.
Multimeters use often two modes Cp and Cs. If loss is high they use Cp. This value is not the value you want. If D is low Cp= Cs but if Cp is high it is not. (1 + D^2 ) x Cp = Cs but in that case your reading will be much lower.
The Peak ( I have) is designed to use down to 10 uF. It will meaure lower but can be way of in that case.
C meters often measure |Z| so ESL and ESR can disturb measurements. The wires of your meters are zero' d for R but the inductors they form are still there. At 1KHz not a problem but some meters use 100 KHz.
A cap on a power supply with no current limiting has two options, first die because the leakage is to high, it heats up and water from the electrolyte gets away. Or you are lucky and there is just enough isolation left to reform again.
I ha one that had double capacity but also to much leakage. This was a rare capacitor, not easy to replace, but after a carefull graduate 24 hour reforming it was perfect again.
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