Using a low current battery bank that is powered by a larger battery bank

I have an ESP32-based project for a device intended to be outdoors unattended for around 6 days. I have used the Sparkfun Low Current Lithium Ion Battery Pack - 2.5Ah (USB) prior with other microcontroller-based projects. However, its capacity is not large enough to make the 6 days. Is it feasible to plug a larger battery bank into the charger of the low-current battery bank to extend the device’s battery life? I believe the low current battery bank has a large enough current draw for charging to keep the larger bank active. However, I fear it would be too inefficient with heat dissipation to achieve a significantly longer battery life. Should I invest in a LiPo-based solution instead?

That should work (not verified with that particular power bank, but I’ve done something similar with other ‘cheap’ ones) though I would strongly recommend switching to a LiPo like this one https://www.sparkfun.com/products/13856

However, its capacity is not large enough to make the 6 days

Have you fully explored sleep options, both for the CPU and the sensors?

Also, that battery pack has a step up converter to produce 5V, which is then stepped down to 3.3V for the ESP32.

About half of the battery capacity is wasted as heat in that process. An 18650 cell with a 3.3V regulator would be significantly more efficient.