The latter is the colloquial definition.
You can use it to refer to any race, but in reality the race you are referring to is only subjective to the user. The server is generally processing all requests in the order they are received.
A race condition usually is referring to a multithreaded system where the threads interfere with each other, causing undesired effects.
Relaxing "race condition" to refer to all causality... is such a loose definition as to give it no meaning at all.
I did a PhD partially on irregular parallelism where understanding race conditions are essential for understanding the topic.
That's literally how 'race condition' is defined in the industry.
You’re not wrong that not all race conditions are harmful, but i feel you’re doing a pretty bad job of explaining what a race condition is.