Supercapacitor is charged via Schottky diode, this current also disable step up booster,
In night or if it lose power booster is automatically started and very effectively discharge
supercapacitor and convert almost all stored energy because can work until 0.3V
Operation TEST
Some assembled pictures:
Circuit is extremely simple to make it reliable.
In your Schematic I see a 10uF capacitor on the output but it is not listed in the BOM/Components.
You also have 4 resistors shown in the Schematic but only three in the BOM/Components. Is R3 needed?