Thanks Roman for the fabulous answer.
If 'media' lies near the patch
It doesn’t actually. It seems to work from wherever I am on my machine.
TLDR: Unlike many other file accessing objects like [soundfile], [reasf~], [textfile], etc. [file] doesn't use search paths¹.
With that footnote, I was hopeful to get [file which] to give me the path of [media/] but no luck.
I’ve also tried to find a way to get [dir] from pdcontrol… I wondered if there was a way to get the path to a given object help, like in SuperCollider
FluidBufAmpGate.class.filenameSymbol
Anyway. Good to know that it is not me. Thanks again for the reply.