"fuse" implies that the CPU will stop working when it is overclocked, this seems to be more of a mechanism for AMD to let them know that the reason the CPU is not working anymore is because it was overclocked and fried.
No, this means something else in chip design. For example, an AVR microcontroller can be configured by blowing some fuses. Here is an introduction: https://www.ladyada.net/learn/avr/fuses.html
Understandable but this is not a fuse in common usage of the word, which is used to break a circuit to protect against over-current. Rather it's an part that changes state irreversibly (much like a fuse would) when something happens. There is no implication that it would cut off the power to the CPU in this sense.
But in the world of electronics fuses and circuit breakers exist to trip when too much voltage is applied to protect the circuit. That's their generally agreed upon definition.
When the Threadripper Pro came out, you could get a machine from Lenovo with 12-16 cores for around $1800 including some ram, ssd, and a gpu. I just checked and now they start at $2800 for a zen 3 TR Pro with 32/1TB/A2000. It doesn’t seem like there is a practical way to build one yourself affordably for Zen 4 or Intel for that matter. A Xeon 3435X and mobo is also around $2500 for 112 lanes.
Lotta manufacturers have done that. I had an Android phone back in the day that was notorious for false positives on the moisture detectors. The phone was a piece of shit and a lot of people wrongly got denied on warranty claims because of supposed moisture.
So the purpose is to protect them if someone overclocks and fries it, meaning they know if you take it in under warranty and say you want this faulty part replaced?
pretty much, also stops any techs or engineers looking into possible problems of the product from spending hours wondering what went wrong before the user says (if at all) "oh yeah, i overclocked it btw".