I have access to our corporate PCF, though both the Apps Manager webpage and the "cf" CLI (and thus the API).
How can I detect what version of PCF they're running? There's nothing in the website that lists it, and the best I can find is using cf api which returns:
api version: 2.98.0
How can I map that to the PCF version, or is there another way to detect it?
I don't believe Apps Manager or the API (i.e. Cloud Controller) will report that information. Both are just single parts of the entire system, so I think you could really only expect them to publish their own version information.
If you want to see versions of what is installed, you need to look at Ops Manager. That will show you the tiles that are installed and each version.
If you don't have access to Ops Manager, you'd need to ask your platform operators.
Hope that helps!