This reply will not help but explain the challenge. Power Delivery negotiates for a common voltage and current, so the device and the powerbank must agree on something in common. As a result it is quite possible for any powerbank and device to not find anything in common and not function. You see this problem fairly often and the only sure way is to test or find someone who has tested.
In your case your device probably is going to only recognize 20V of which it can draw up to 1.5A. The powerbank you have is "PD Output: 5V=3A, 9V=2.6A, 15V=1.6A" so you see it supports only 3 levels and does not do 20V which is the one voltage we know your Dell is expecting.
Who's fault is this? Well a bit of both, Dell, if had made your device support say 15V, then it would have overlapped Anker, but if Anker had supported 20V they'd also overlap.
It is electrically less efficient for Anker to support higher voltage, it has to step up from 3.7V by a bigger factor so this is overall more the fault of Dell who could have made the laptop accept lower voltages. The smaller powerbanks have fewer cells and so has fewer options for higher voltages, e.g. 20000 is made up 6 3.7V 3400 18650 cells. They probably are using 3 parallel 2 series so would be 7.2V from which they can step down to 5V or up to 15V. Chances are the battery in your Dell has 18V-19V cells so it refuses to accept anything less than 20V. Dell's stance is the similar opposite problem of Anker, Dell would have to step up from less than 20V to recharge its battery and electrically that would add a little extra cost.
Nightmare, I know.
You asked if something will work, well within the caveat there is no guarantee, if you look at the 26800 PD product's specs you do see 20V listed
This supports the 3 levels of the powerbank you have plus a 4th level of 20V.
Chances are the bigger powerbanks is capable of higher voltage, such as they are running more cells in series to be a higher voltage than the smaller 20000. The 26800 is likely 8 3.7V 18650 where the also are likely wired 2 parallel of 4 series to make 7.2V but they elected to step up to 20V as they had more current to play with.
It isn't really fully Anker's fault, but Anker has excellent customer service and likely will positively respond to a warranty claim. You're more likely to find the 26800 to work but it is also not a guarantee as its also up to Dell to support PD and support more modes.
FWIW I also have a PD input laptop and it doesn't work with the one PD output charger but I got both for free so I am wiser and not poorer. I have sitting this problem out for 2018 on items I did spend money, on 2015's technology of a common denominator more universal to work of 5V 2A. My portable device is the Pixel C and it recharges with everything Anker sells of which I have the 5V output version of the 26800.