I'm fascinated by the design of the rewinder. Could someone provide me with some guidance on where to begin learning how to design a board like this?
The trickiest parts here are dealing with the MCU (look for example schematics to copy, they're probably already in the datasheet), sourcing parts (Mouser/Farnell/Arrow are expensive but have good search tools - LCSC is dirt cheap but has terrible search), and soldering the PCB (stick with through-hole parts, if at all possible). You can get a bare PCB of this size made at JLCPCB or a dozen other places for less than $5 - not including shipping.
> stick with through-hole parts, if at all possible
These days it's more work to avoid SMD than it is to embrace it. Many many parts are not available in through-hole, and dealing with 0805 passives and 0.65mm pitch ICs is not that difficult (unless you assume that it is).
As a bonus, you get much easier re-work, access to assembly services, and cheaper components.