What is best for battery depends on your goals.
The way to keep a battery life longest is keep it around 70% charged. What ages a battery is non-use, using it a lot, cold, heat. Cells have a 500 depth recharge capacity, so if you drained a laptop fully then recharged, it would do it 500 times, so if you did that daily, 18 months. If you drained it 50% then full, you’d get 3 years, if you kept it between 60% and 80% you’d get years. Cells don’t like heat and keeping a cell 85%-100% makes it hotter so that ages faster too. Another way to not age is keep at 100% all the time so the depth cycles never get touched and no heat from recharging. Make sense?
For this conceived use case of being off-grid for many days, for at least long periods between access to wall sockets, you’d want to start the period with everything fully charged, then connect the Powercore to laptop, drain the Powercore, then drain the laptop’s battery. The reason is there is energy lost in the chemical process of storing energy in the battery, so if you have battery recharging battery then being used, the energy passes through batteries twice, so double the energy loss from chemistry, vs if you drained the Powercore first then laptop, you have a single loss of energy from chemistry. By all means do a benchmark when you test it all.
I’d be sceptical of any vendor’s claims. Anker’s customer service and reliability is high and a good brand to rely on. But the electronics contained within are all very similar, and a buck-boost converter is most efficient when not exceeding a factor of 2 on voltage. So to get 20V out, the electronics probably won’t have less than 9V cells (e.g. 3 cells in series, and 2 of them in parallel) so probably won’t be recharged on less than 9V. 9V is unsafe to electronics which can only take 5V, hence Power Delivery has a negotiation.
What you ideally want is some luck. Luck would be if your laptop can actually recharge off less than 20V, anything helps, like it did 9V would be very useful. You then need luck to find something which ingests 5V non-PD in and gives that voltage out. Anker does make 5V in 9V out Powercore. Best way to get luck is ask Anker and buy from places with no-quibble free return so you can test. The Powercore 20000 PD Essential does take 5V non-PD in and gives 9V PD out, so if your laptop accepted 9V PD then voila!