How to tag test tracks for automobiles?

Motor companies, some universities and institutes have their own tracks.
They looks like racing track but aren’t intended for racing.

Can I tag them “highway=raceway”?

It looks like you answered that question with your statement above it. If it isn’t a raceway, you shouldn’t tag it as a raceway.

I haven’t had to map one of these myself, but I think I would use highway=service + access=private. I can’t think of a more specific tag off the top of my head.

A few examples:

There’s ~130 service=test_track instances.