ESR measurements Capacitors

Maybe the real issue is that the meter has no professional specs, or has been checked against some benchmark standards. So the assessment has no validity even for 'simple' comparisons?
Nevertheless, comparative measurements between different capacitors will be valid. There is no issue with the instrument, instead there is a big issue with the paper-in-snake-oil capacitor.
 
The accuracy specification in the manual indicates the ESR tolerance range for a 1uF cap is +/- 0.07 for most of the measurement frequencies, increasing to +/-0.10 at 10kHz and seemingly reducing at 100kHz.

That would indicate that all ESR measurements with a value of 0.12 or less are effectively 'the same' unless measurements can show that measured ESR can be seen to behave as anticipated for low levels. Perhaps one way to check operation would be to measure 2 or 3 caps of the same model/value, and then measure them again when soldered in series (or parallel for high value readings). Another way would be to check with a low resistance surface mount or 0.25W resistor soldered in series.