For this contest, I looked around the market and considered the charging ICs for supercapacitors. There are a lot of different charge ICs, but most of them have a significant disadvantage: they are not so easy to solder with a (slightly advanced) home soldering iron system.
Excursus: Why do I need a charge IC?
Here is a look into an application note from TI that helps us answer the question:
"Most super capacitors (supercaps) can be discharged down to 0 V and recharged to their maximum voltage with the manufacturer recommended charge current. A simple voltage regulating LED driver with constant current, usually regulated by sensing a low side, series current sense resistor, then a voltage clamp can be used to charge a super capacitor. However, using a dedicated charging IC that provides both output voltage and current regulation, as well as input power regulation, temperature sensing, thermal regulation and other safety features allows for more precise and safer charging. Also, there is no series sense resistor creating an undesirable voltage drop, especially during discharge."
(Source: https://www.ti.com/lit/an/sluaao7/sluaao7.pdf?ts=1695069242279&ref_url=https%253A%252F%252Fsearch.yahoo.com%252F )
About the charging ICs
A look at ADI's Supercapacitor Chargers page shows that, with one exception, we don't actually find any components here that are easy to solder.
Here you can find many QFN or DFN packages. With MSOP there is usually an EPad under the component. So for me, there is unfortunately nothing here.
At TI it looks unfortunately not so much better: https://www.ti.com/power-management/battery-management/charger-ics/products.html#338=SuperCap&sort=338;asc&
Here you can find only xQFN, WSON and VSON packages. This requires a solder paste stencil and a reflow oven. This is again too much work for me.
I also found charge ICs at the company e-peas, which combine the connection of solar cells and ultra caps. Unfortunately, the packages are not very maker-friendly. For example, the ARM10330 https://e-peas.com/product/aem10330/ device has a QFN40 package, which again requires a solder paste stencil and a reflow oven.
If the soldering problem could be solved, I would like to design-in this device.
My second favourite is the very interesting load IC is the MP5493 from MPS (https://www.monolithicpower.com/en/mp5493.html ). It has a reasonably well-solderable TSOT23-8 package. But now comes a but: so the datasheet hides behind a login, which is only accessible for professional users. Furthermore, the datasheet is still in a rather early state and leaves some circuit points open. Therefore, this component is unfortunately out of the question for Maker.