I wanted to make sure my computer stays connected to my router in case the loose LAN cable gets pulled out by my pets roaming around.

Instead of spending money$ on a new cable like a normal person would, I spent countless hours researching for the right keywords, and found the perfect free solution - apparently it's called "bonding" and allows Linux to gracefully fall back from Ethernet to WiFi, all while having a single IP address:
https://wiki.debian.org/Bonding#Configuration_-_Example_2_.28.22Laptop-Mode.22.29