No, spinning is an accelerated reference frame. If you spin on a carousel, you won’t feel the same as standing still.
Now what does it mean for a black hole, which we assume to be a singularity occupying no space at all, to be spinning? We don’t know. That’s one of the gaps in our theory. But as the collapsed remnants of an object that was spinning, they should have done residual angular momentum.
Not necessarily. The three definitions for a "spinning" black hole that I gave upthread do not require the presence of any accelerated frames or observers.
> what does it mean for a black hole, which we assume to be a singularity occupying no space at all
This is not correct. A black hole is a finite region of spacetime enclosed by an event horizon. The singularity is inside the hole but is not all of the hole.
> to be spinning? We don’t know.
Yes, we do. We have known since the 1960s that the Kerr solution to the Einstein Field Equation describes a spinning black hole, and all of the geometric properties of that solution have been known for almost as long as that.
> That’s one of the gaps in our theory.
No, it's not. See above.
> as the collapsed remnants of an object that was spinning, they should have done residual angular momentum.
This is correct, but it does not imply or support your other claims.
You're missing the point that, since a black hole is purely made of spacetime geometry, there is no "mechanistic explanation" of its spin in the sense you mean.
Now what does it mean for a black hole, which we assume to be a singularity occupying no space at all, to be spinning? We don’t know. That’s one of the gaps in our theory. But as the collapsed remnants of an object that was spinning, they should have done residual angular momentum.