The earth's rotation imparts to the rocket a free delta V of roughly 450 m/s if you launch straight eastward.
About 464 m/s for eastward launch from the equator; it's less than that at higher latitudes (proportional to the cosine of the latitude), about 400 m/s from Canaveral, and less again if launching into higher inclinations.
If you launch westward instead, for a retrograde orbit inclination of 123 deg out of Vandenberg, say, it seems you lose that free delta V.
But is this correct? Are westward launches more expensive in fuel than eastward launches?
Yes. The total delta-V budget to eastbound LEO is usually about 9200-9500 m/s, varying with the exact trajectory, so a pure westward retrograde orbit would be about 8.5% more expensive.
Is the earth's free delta V normally included in the velocities reported during launch?
Depends on who's reporting, and why. For information reported to the public during launch, it's more intuitive to start with surface-relative velocity (it would be confusing to say the rocket is moving at 400 meters per second just as it begins to move), but at some point during ascent when atmospheric resistance is no longer as relevant (the atmosphere moving, roughly, at the same speed as the surface) it makes more sense to report velocity in Earth's non-rotating frame instead.
I don't know if e.g. SpaceX blends between reporting surface-relative and non-rotating velocity during ascent, or switches over hard at some point.