Calculating ESR of a capacitor
Suppose I want to calculate the ESR @ 100 kHz for the 220 µF capacitor :

You can't just use the \$\mathrm{tan\delta}\$ value, which is mostly given for 120Hz in the datasheets, for calculating ESR at 100kHz. Because, as it's described in the calculation method, the equivalent series inductance, L, is neglected at frequencies up to 1kHz.
ESR values given in the datasheets are not calculated values. They are measured at the factory/production. And the measurements include the effect of L and r. That's why your calculations and the datasheet values don't match.