I took an ESP-01S module and a couple of part used AA batteries and left it to run sat on my mesh network until it stopped responding.
This won't be the first time somebody has tried this kind of thing but I was impressed it worked down until almost 1.8v. It ran for ten hours on a pair of batteries that weren't great to begin with, coming in at 2.7v when I started.
It would have been sending packets every few seconds all this time, so it's not like it was sat there doing nothing. I know my code currently causes quite heavy power use, averaging at about 80mA.
This is telling me that my aspiration to run a wearable mesh node 'all day' on normal alkaline batteries is almost certainly achievable. A twin AA battery box is not egregiously large, I can probably desolder the onboard LEDs in a final version and maybe improvements in power management in the code will have some effect.
Of course I'm currently ignoring that I want to connect a GPS module to the wearable and this will eat a consequential amount of power, but I'll worry about that later.
A LiPo battery is what most people would go with but I prefer the wearables to have field replaceable batteries. This is because they will literally be used in a field/forest, the sort of place where you worry about being able to charge your phone as the evening draws in. Having a few AAs to hand is very easy to manage if something goes flat.
For my next experiment along these lines I'll try the same with a 18650 cell and 3.3v regulator. If AAs won't cut it 18650 cells are the sane removable LiPo option in my opinion. There are also 14500 cells which are AA sized so very convenient but these have a much lower capacity.