How do I register a tabhook with the new interface? Is it even possible?
Yes. By $this->provideHook('Icingadb/Tab') and a class in the usual place.
Is there a simple/example plugin for icingadbweb similar to the pnp module?
No. Not yet.
My plugin seems to show up in some legacy mode (via CompatObject).
Icinga DB Web currently doesn’t even support the legacy integration of Monitoring/ObjectDetailsTab hooks. So I don’t know how you got that error. Which hook are you actually using?