So if you are aiming for results and not just a fun learning project, then I would simplify some of this.

The WS2812 style LEDs are great if you want to have every individual light be individually addressable (like having animated light strips). However in this case you really just want a static white light (probably dimmable so you can tune power usage) so you can get a simpler and cheaper strip like this. This would also free us from needing a more complex controller like an arduino. There are usually also varying degrees of waterproofed strips depending on how exposed you expect these strips to be.

These should include a controller so you can set the brightness to something reasonable (you could usually go 1/4 or less the max and still be plenty bright while saving power).

Since you want it to turn on at night, you can get a photo sensor that automatically trips on when the ambient light level drops below a certain amount.

Note that these are actually all using 12v power. You can either just power it off a 12v deep cycle or use a step up converter to boost what are probably 5v lipos. Also make sure you size your components and wiring for the total amp draw of your lights. I suspect a chicken coop is quite small, but I am a city boy and don’t know any better. But basically if you are using a single strip or less, the you are golden.

You could charge either battery pack off solar, but that depends on the solar panel and charger you have (and is it’s own can of beans).

This is all actually pretty similar to a light set up I did for burning man one year, and if I could get to work half drunk and completely heat exhausted in a desert, then I have confidence anyone can handle this if they give it a try.