How to optimise battery usage on modern electronics? What is the best way to use an external power bank with a modern smart phone or similar device if the goal is to get as much usage out of the combination?

Premises:


The devices has a battery of 2 Ah and the power bank's capacity is 10 Ah
As I understand it, a rule of thumb is that the thermal efficiency η when charging a battery is about 50 %. That is, charging the power bank from (1) requires 20 Ah.


With 1 and 2 in mind, the power bank could charge the phone from 0 to 100 % 2.5 times.

Therefore, my question is: wouldn't it be better to keep the power bank attached to the phone all the time to keep the phone at 100 % as long as possible rather than using it to charge the phone when the battery is half empty or so? My idea is that keeping the power bank attached all the time would make η ≈ 100 % since the phone's battery would just "pass by" the current from the power bank. Am I right?
There is always some internal resistance in a battery. All other things being kept constant, the larger the battery, the less internal resistance, so less energy is wasted inside a larger battery due to internal heating and energy loss.

This is particularly important in high-drain devices such as phones and laptops, where batteries are discharged in just a few hours. By having the power bank in parallel, the load is shared and batteries are being drained over a longer time.

For example, a once-cell penlight with an incandescent lamp might burn for an hour. Two cells, one replacing the other, would then last two hours. But two cells in parallel might last 2.2 hours, because of the lower internal resistance and decreased energy waste in the cells.