Ever since I got my kid the Lego Robot Inventors 51515 kit, I have been looking for a good way to store the pieces and I think I have finally found the solution thanks to www.RoboticsLearning.com!
On that website, I found a link to a storage organizer system sold at Harbor Freight: Storehouse Toolbox organizer with 4 drawers. If you dont have a harbor freight near you, I think these from Amazon are similar organizer systems:
Here are some images of my organized 51515 kit:
https://photos.app.goo.gl/bxrgZ6fAAvpn5eyG7
Here is where you can buy the labels ($10 for the PDF) and find more information on RoboticsLearning.com: LEGO Robot Inventor Set Case Label PDF Files (roboticslearning.com)
Update (11/29/2022): Here is how you can use the above storage box to organize the Spike Prime Kit: https://docs.google.com/presentation/d/10Esa5g_wjFTve83ESnl0FsqPti4y4rMp9Yz4-k-3rP4/edit?usp=sharing