> Its signal will become indistinguishable from background radiation at a distance of slightly over 625 light years.
Doesn't that depend on how large the receiving antenna is, because the larger the antenna the smaller the source angle you can focus on and the less background radiation will be in that source angle ?
The converse: any life out there trying their best to communicate with us, beyond 600 ly... we wouldn't realize it even if we happened to catch (what's left of) the signal.