What spectral type of star has an absolute magnitude of exactly 0? We know that Vega is the star that serves as the zero point for the UBV color scale, and has an apparent magnitude of nearly zero (+0.02). But its absolute magnitude is +0.58, making it rather far from $M=0$. So what spectral type would have an absolute magnitude of $0 \pm0.02$, and are there any stars that satisfy this?
There isn't a one-to-one relationship between spectral type and absolute magnitude.
Instead, there is a mean relationship with a fair bit of scatter around it. The reason is that the luminosity of a star of a given effective temperature depends on its composition/metallicity and how far along in its main sequence lifetime it is.
Basically, late B-type main sequence stars (say B7/B8V) have an absolute magnitude of about zero. Alternatively there are low mass stars ascending the hydrogen shell burning giant branch (types of about K2-K5 III) that would have an absolute magnitude of zero.