The issue is that during the day when its cloudy solar panels provide only 3V, but the "Solar Lipo Charger Board CN3065" expects input of 4.4V-6V.
Is that 3V the open circuit voltage on a cloudy day? Did you measure it? If not, where did that number come from? And by the way, the low voltage lockout is 3.7V, not 4.4V, so I wouldn't take the 4.4V too literally - you would have to test it.
A solar panel will supply as much current as it can at the voltage needed by the charger, but that's only if that voltage is below the open circuit voltage for the illumination level of the sun at the moment. So even if the full charge current isn't supplied, your panels could still supply some current. But the bottom line is that on a cloudy day, the panels won't contribute very much, and wouldn't contribute much if it were an MPPT charger. So you need enough bright sunny days to keep the battery charged.
Also, you didn't say, but you also need a very low dropout 3.3V regulator for your STM. The panels may be nominal 5V, but that typically means they can put out close to 6V in bright sun.
Do you have any feel for how much current your circuit will draw when running? Will it be sleeping part of the time? That's going to be the biggest determinant of battery life.
I have tested a circuit similar to this that used a TP4056 charger, which is not a "solar" charger, and it worked pretty well. But you need to get the panels in direct sunlight as much as possible.
Edit: You may do better using a single 500ma solar panel. If you use multiple panels, you may have to put diodes in the outputs to prevent back feeding from one to another, and those diodes will have a voltage drop.