This project is kind of in a failed state at the moment.
The ESP-01 suffers from a "brown-out" kind of condition where it doesn't work right unless I short/start it from 0 to 3.3V (pulling the ESP-01 out of the socket and plugging it back in) after the super caps have been charged/3.3V is available after the LDO.
I have a circuit in the works (low-dropout voltage regulator), I got help on it.
The issue is the parts are so small... the 0.1uF capacitors for example are like the size of a pin head.
I ordered the parts but I gotta put it together/see that it works. It's also super complicated/kind of goes against the design of this thing where it was supposed to be "stupid simple".
If you don't want to use a energy-harvesting optimised charging controller to get the energy from the solar panels to the Caps, you should use an ideal diode controller to replace the 1N4007