"Would you still be spinning? Relative to what?"
If Space-Time was still part of the Universe that you found yourself in, then Gravity would still be the dominate force and you would still be spinning, relative to the mass bending the Space-Time affecting you.
Also spinning in a vacuum provides no friction so you would spin forever unless acted upon by a different force.
You would still spin, but wouldn't have a reference point to know that you were spinning. Except, for maybe your inner ear would tell you.. maybe
When you consider for a moment that centrifugal force is generated when you spin. The more spin the greater the force, you could be spinning so slow you may never notice or so fast that you might be glad you don't have a reference point to look at. With slow spins your inner ear may not be effected at all, whereas with higher spins it would be.
One of the discoveries of recent physics (past several decades) is that space isn't nothingness. So-called "empty space" is only empty of matter, but it isn't empty in terms of subatomic particles, which are constantly coming into and passing out of existence. So, space is actually a kind of "stuff." A stuff you can spin in reference to.
Would you still be spinning?
Relative to what?
Yourself, a moment ago.
Why is the title in ALL CAPS? It makes this feel like a sensationalised discussion, but it's not.
Here's a relevant article: Why Rotation Makes No Sense Sometimes
Like you say, there's something more to empty space than nothing... entanglement seems to prove instant "connections" of some kind across vast distances or nearby in a higher dimension. God, I hate sounding like another Doctor Woo. Difference is, I'm not declaring that this higher dimension or whatever it is actually exists, or that it explains other mysteries I want answers to. We just don't understand its mechanism, yet.
Space-time and gravity only exist as an artifact of the matter that permeates it. Bottom line: all motion is relative, so even if the observer is a material entity, space-time/gravity does not exist without other material entities with which to interact. Therefore, spinning is a meaningless concept in a universe devoid of interacting, material entities.
So, if your arms are out, blood will not rush to your fingertips and you won't get dizzy without another massive object with which to interact? There will be no evidence or sensation of spinning?
So-called "centrifugal force" isn't a physical force. The physical forces are "gravitational,electromagnetic, strong nuclear, and weak nuclear. Each one is described mathematically as a field. The gravitational force is modelled as a continuous classical field." (source)
It only works for spherical chickens in a vacuum.