I've done the opposite to a lot of riders - I had a chainset of unknown mileage and rather than guess, I simply rode the whole thing into the ground.
Shifting got progressively worse over time, but it wasn't linear. There were certain gear combinations that slipped more under normal load, and others that slipped under heavy load.
Climbing a grade became risky, a good steep ramp could see me slip. So I learned that climbing seated (or very close to the saddle) was a wise plan.
Toward the end, the gears could slip when taking off from stopped, or when putting in some power to accelerate.
At this time I changed everything, chain, cassette, chainring, inner/outer cables, and both jockey wheels. Even though the old cassette was ultegra and other parts were 105, replacing with the lowest cost (tiagra?) components was a phenomenal upgrade in shifting accuracy and snappiness.
I also changed brake pads and cables, and bartape because the old stuff was a bit thin and didn't survive removal.
There's no gain to replacing only the chain if its already significantly elongated. The cassette will be worn to suit, so all you do is get worse shifting and drastically accelerate the wear of your new chain.
So in summary - wear is a gradual degradation process that you might not notice over time.