Do Apple Airpods Support HSP? For reference I am trying to connect them as a headset on linux (where HSP is supported by PulseAudio and HFP requires more work). When I connect them, my bluetooth manager reports an entry for HFP, but I do not see an entry for HSP.

I'm not asking about how to actually connect them, but rather whether HSP is supported given that it seems to be a subset of HFP.
If you look at the Bluetooth diagnostics in System Profiler on a Mac, you'll find that the AirPods are listed as offering the "Handsfree" service, not the "Hand-set" service. 

The full list of services supported are: Handsfree, Wireless iAP, AVRCP Controller, Audio Sink, AVRCP Target, AAP Server.

For the Pro model things are a bit different.