What is the model of ESR meter you're using?
The 0.1 uF capacitor I have in my assortment is marked with the manufacturer--it's Jwco.I found the manufacturer's list of capacitor models here: http://www.jiaweicheng.com/en/productlist/products.html
They show several models whose capacitance range goes down to 0.1 uF. My capacitor doesn't have the series designator marked on the capacitor, so I chose the LF series to look at: http://www.jiaweicheng.com/Data/jiaweicheng/upload/file/20151126/LF(1).pdf
For some reason they only show down to 0.47 uF at 50 volts even though the first web page says that the LF series goes down to 0.1 uF. They do show the maximum impedance for the 0.47 uF 50 volt capacitor as 5.4 ohms. This is much less than the 23 ohms for the Nichicon data that you found.
Here is a list of various ESR information, including descriptions of how ESR meters work. The link you gave for the meter you constructed also describes how it works. All of these simple ESR meters actually measure the impedance magnitude, not the actual ESR. As explained here: https://www.midwestdevices.com/pdfs/Tnote3.pdf
this technique only works if the capacitance to be measured is large enough that its reactance is significantly less than its ESR at the measurement frequency. This means that as a practical matter the capacitance should be larger than 1 uF if the measurement frequency is 100 kHz.
However, if a small 0.1 uF capacitor is very bad, meaning that its ESR has become much higher than its reactance, the simple ESR meter will show this, and a truly defective capacitor will be detected.
You said that your capacitor measures more than 10 ohms, but you haven't said how much more. If the capacitance of your capacitor is exactly 0.1 uF, its reactance would be 15.9 ohms, and if its ESR is much lower than that, its impedance would be almost the same as its reactance--just a little more than 15.9 ohms.
But another complication is that the capacitance of electrolytic capacitors decreases at high frequencies. Manufacturers specify the capacitance at a frequency of 120 Hz (or possibly 100 Hz). But ESR meters measure at 100 kHz; if the capacitance is lower at 100 kHz than at 120 Hz, the reactance will be higher. Your capacitor is probably less than 0.1 Hz at 100 kHz. Since the ESR meter can't give a reading less than the reactance, it is to be expected that the reading for your capacitor (even if it's not defective) will be greater even than 15.9 ohms.
A reading for your capacitor somewhat greater than 15.9 ohms would be indicative of a good 0.1 uF capacitor.
Using an impedance analyzer we can see how the impedance of my new 0.1 uF capacitor varies with frequency. Here is an image showing the impedance (green curve) and ESR (yellow curve) for a frequency range from 100 Hz to 5 MHz. The bottom of the graph is 1 ohm, and the top is 1000 ohms. There are two markers, marker A at 100 Hz, and marker B at 101.7 kHz (essentially 100 kHz). The values of impedance and ESR at those two frequencies are shown in the upper right of the image. The impedance magnitude of my 0.1 uF capacitor is 19.7 ohms at 100 kHz, and its ESR is 3.77 ohms at 100 kHz:
I have a commercially available ESR meter, Model MESR-100, which uses the impedance measuring technique just like your meter. For this capacitor it gives a reading of 21 ohms, which is close to the value 19.7 ohms the impedance analyzer got, and quite different from the true ESR of 3.77 ohms.
But just knowing that the impedance is not many times greater than the reactance suggests that the capacitor is not defective.