The Higgs Boson has spin 0. See https://en.wikipedia.org/wiki/Scalar_boson

Is using quantum mechanical spin a fair comparison? Isn't it moving the goalposts a bit?

> As the name suggests, spin was originally conceived as the rotation of a particle around some axis. Historically orbital angular momentum related to particle orbits. While the names based on mechanical models have survived, the physical explanation has not. Quantization fundamentally alters the character of both spin and orbital angular momentum.

> The classical analog for quantum spin is a circulation of energy or momentum-density in the particle wave field: "spin is essential a wave property".

https://en.wikipedia.org/wiki/Spin_(physics)

I thought quantum mechanical spin is completely unrelated to Newtonian angular momentum, but IANAP.

Its not completely unrelated, but it is not clearly related. That is, spin contributes to overall angular momentum, but that contribution is much too large to be explained as the actual rotation of subatomic particles. So, like most quantum properties, our Newtonian intuitions are poor guides.

Any tidally locked satellite such as the moon.

A tidally locked satellite rotates: one rotation per orbit.

unless the body it rotates around rotates at the exact same speed around another body in the opposite direction

Then it still rotates.

It can only rotate relative to an arbitrary point, not in some objective absolute sense. Here it does not rotate relative to chosen point.

Something about privileged reference frames...

But what's the alternative, right?

A Pulsar, that's not really spinning but oscillating back and forth, becoming a very highly precise instrument of time measurement as well:

https://physicsworld.com/a/pulsar-timekeepers-measure-up-to-...

Pulsars are dense compact spinning objects.

From your link: "Pulsars are neutron stars that rotate at very high speeds and appear to emit radio pulses at extremely regular intervals. The pulses are actually all we see of a radio beam that is focused by the star’s magnetic field and swept around like a lighthouse beacon."