SuperCap Charging and Delivery System using Solar Panels

A super cap is not a battery.
A super cap discharging voltage drops steeply. A rechargeable battery keeps its voltage up until it is nearly dead.

 

It might help if we knew more about your project, for example why the need for supercapacitors and why you settled on using 3 of them and 3x 5V, 250mA solar panels, and what you seek to do with the microcontroller and voltage monitor.

Regardless, the solar panels are not a constant 5V, depending on the accuracy (and how) they're rated it may vary from that. Generally you want to keep voltage as high as possible to reduce vDrop losses when there's a charging regulation and delivery regulation involved.

With what you have, this limits you to 3 x 2.7V caps in series for (max) 8.1V and 100F capacitor bank. 2x series of 5V solar panels might achieve this (then you have one solar panel left over), or 3X in series, then you need a charge controller limiting output to the capacitor bank 8.1V or lower.

Since using solar cells and capacitors is somewhat of an intermediate length charge/discharge cycle based on sun, vs night, vs use of the 5V to modules, I am wondering why you feel supercapacitors are the better choice than a smaller, more cost effective battery? I mean I could see the supercapacitor purpose for a very high charge and discharge rate but that doesn't seem to be the scenario with a few hundred mA of solar power.

Anyway you could then use a boost/buck rather than a buck/boost, or just a buck if you accept some capacity loss.

I recommend that you start over and define the task then the best way to accomplish it rather than "I have a spoon, three fiddles and a gnome, what's the proper way to play Beethoven."