For those who want to go the High Side Switch route.
With the IC on a small board (take care you know what you are doing) soldered and two 1/8 watt resistors you are almost there.

On the Lilygo I soldered the other 1/8 Watt resistor, the 3 x 1N4148 diodes and the wires.

With one switch (push button or Normally Open reed contact) you can control the Lilygo in a regular way.
With no High Side Switch the Lilygo uses around 80 micro amps when OFF.
This is with no SD card but 16 Mb memory IC fitted.
When switched OFF with a High Side Switch the Lilygo uses around 30 micro amps.
It doesnt matter if you use a SD card or only onboard memory.
So this is almost three times less, making the time before you need to recharge 3 times longer.
Now if you find this not enough there is an other full electronic switch option.
This option needs an extra switch button or Normally Open reed contact but gives an OFF state current use of 0,2 micro ampere.
Yes, this means that the self discharge of the lipo is likely larger then the power drain from the switch.
All used and tested with firmware version 6.00
I heard the NAND memory from Alhop also works now. So more options.....
Paco