The short answer
Depending on scale and location, developments hundreds of metres away can still have a meaningful impact.
There's no fixed radius that makes a development irrelevant. A large-scale scheme can affect an area well beyond its immediate footprint, which is why proximity checks need to look wider than the neighbouring plots.
Why this matters for your purchase
This is why PropM8's planning constraints check looks beyond the immediate neighbours. It's built to catch the kind of scheme that's easy to miss on a viewing but shows up in the data.