Hi Angelo,
sorry for the late reply.
With a Pico you can measure a battery voltage (see this tutorial: Raspberry PI Pico Battery Checker), but I don’t know how much this can be realiabe as it will measure a battery voltage while from the same battery which is powering the Pico.

Hi Nico, can you please try to fully charge the battery alone, connect the Pico and then removing (or covering) the solar panel? My doubt is if tour Pico and sensors use all the energy from solar panel and if there’s actually no room for battery charging

I followed the same steps here as you did with this tutorial. Now I have come across an issue which I cannot explain.
I connected the wires from the TP4056 (same as yours) to the battery and the raspberry pico. To check if it works, the pico turns it own led light on.
During sunrise, the pico wont turn on unless i plug the vsys and gnd again (after plugging them out). Then the led shines a light
At sunset (when the solar panel doesn’t provide energy) the raspberry pico led light is flickering, indicating it is turning on and off again. I do not use a breadboard. Have you tried this setup for a longer time (24h)? And do you have an idea why this doesn’t work at mine?